From fd8cc0c7bce2fba118fc77fff5c28ddb32335967 Mon Sep 17 00:00:00 2001 From: Praveen Nair Date: Tue, 28 May 2024 22:01:26 -0700 Subject: [PATCH 1/2] Add WI24 final practice --- README.md | 6 +- assets/images/wi24-final/bow.png | Bin 0 -> 58496 bytes assets/images/wi24-final/confusion.png | Bin 0 -> 47608 bytes assets/images/wi24-final/hotels.png | Bin 0 -> 180221 bytes assets/images/wi24-final/validation.png | Bin 0 -> 107239 bytes docs/assets/images/wi23-final/q3.png | Bin 188538 -> 0 bytes docs/assets/images/wi23-final/q4.png | Bin 137147 -> 0 bytes docs/assets/images/wi23-final/q6.png | Bin 285917 -> 0 bytes docs/assets/images/wi23-final/q6_density.png | Bin 196281 -> 0 bytes docs/assets/images/wi23-final/q7.png | Bin 469923 -> 0 bytes docs/assets/images/wi23-final/q9.png | Bin 198207 -> 0 bytes docs/assets/images/wi24-final/bow.png | Bin 0 -> 58496 bytes docs/assets/images/wi24-final/confusion.png | Bin 0 -> 47608 bytes docs/assets/images/wi24-final/hotels.png | Bin 0 -> 180221 bytes docs/assets/images/wi24-final/validation.png | Bin 0 -> 107239 bytes docs/fa21-final/index.html | 58 +- docs/fa22-final/index.html | 48 +- docs/fa23-final/index.html | 19 +- docs/index.html | 15 +- docs/sp22-final/index.html | 56 +- docs/sp23-final/index.html | 71 +- docs/sp23-midterm/index.html | 180 -- docs/wi24-final/index.html | 2101 ++++++++++++++++++ docs/wi24-midterm/index.html | 57 +- index.md | 12 +- pages/exams/sp23-midterm.yml | 11 - pages/exams/wi24-final.yml | 18 + problems/wi24-final/wi24-final-data-info.md | 17 + problems/wi24-final/wi24-final-q01.md | 152 ++ problems/wi24-final/wi24-final-q02.md | 179 ++ problems/wi24-final/wi24-final-q03.md | 88 + problems/wi24-final/wi24-final-q04.md | 88 + problems/wi24-final/wi24-final-q05.md | 85 + problems/wi24-final/wi24-final-q06.md | 47 + problems/wi24-final/wi24-final-q07.md | 37 + problems/wi24-final/wi24-final-q08.md | 87 + problems/wi24-final/wi24-final-q09.md | 120 + problems/wi24-final/wi24-final-q10.md | 78 + problems/wi24-final/wi24-final-q11.md | 94 + problems/wi24-final/wi24-final-q12.md | 102 + 40 files changed, 3473 insertions(+), 353 deletions(-) create mode 100644 assets/images/wi24-final/bow.png create mode 100644 assets/images/wi24-final/confusion.png create mode 100644 assets/images/wi24-final/hotels.png create mode 100644 assets/images/wi24-final/validation.png delete mode 100644 docs/assets/images/wi23-final/q3.png delete mode 100644 docs/assets/images/wi23-final/q4.png delete mode 100644 docs/assets/images/wi23-final/q6.png delete mode 100644 docs/assets/images/wi23-final/q6_density.png delete mode 100644 docs/assets/images/wi23-final/q7.png delete mode 100644 docs/assets/images/wi23-final/q9.png create mode 100644 docs/assets/images/wi24-final/bow.png create mode 100644 docs/assets/images/wi24-final/confusion.png create mode 100644 docs/assets/images/wi24-final/hotels.png create mode 100644 docs/assets/images/wi24-final/validation.png delete mode 100644 docs/sp23-midterm/index.html create mode 100644 docs/wi24-final/index.html delete mode 100644 pages/exams/sp23-midterm.yml create mode 100644 pages/exams/wi24-final.yml create mode 100644 problems/wi24-final/wi24-final-data-info.md create mode 100644 problems/wi24-final/wi24-final-q01.md create mode 100644 problems/wi24-final/wi24-final-q02.md create mode 100644 problems/wi24-final/wi24-final-q03.md create mode 100644 problems/wi24-final/wi24-final-q04.md create mode 100644 problems/wi24-final/wi24-final-q05.md create mode 100644 problems/wi24-final/wi24-final-q06.md create mode 100644 problems/wi24-final/wi24-final-q07.md create mode 100644 problems/wi24-final/wi24-final-q08.md create mode 100644 problems/wi24-final/wi24-final-q09.md create mode 100644 problems/wi24-final/wi24-final-q10.md create mode 100644 problems/wi24-final/wi24-final-q11.md create mode 100644 problems/wi24-final/wi24-final-q12.md diff --git a/README.md b/README.md index f0d41b2..0781ae1 100644 --- a/README.md +++ b/README.md @@ -1,6 +1,6 @@ -# practice.dsc10.com +# practice.dsc80.com -Repository containing practice problems for DSC 10 (past exams and discussion). Hosted at practice.dsc10.com. Before using the repo, make sure you have the following packages installed: +Repository containing practice problems for DSC 80 (past exams and discussion). Hosted at practice.dsc80.com. Before using the repo, make sure you have the following packages installed: ``` - BeautifulSoup4 @@ -45,7 +45,5 @@ To explain up-front: - What ( ) and [ ] mean. In their absence, students needed to write out code by hand. - In-person means on-paper. - Think of select-all questions as a sequence of true-false questions. Partial credit for these questions was assigned accordingly. -- When taking an exam for practice, we recommend having a copy of the DSC 10 reference sheet open in another tab, as well as a second copy of the exam, so you can access the data descriptions. - diff --git a/assets/images/wi24-final/bow.png b/assets/images/wi24-final/bow.png new file mode 100644 index 0000000000000000000000000000000000000000..6555153931d9973da7e3096328ba8df71163f8b0 GIT binary patch literal 58496 zcmeFZ_cvW#+da-fqC`lvAUKJLPNF6RClN&NokN5mTB7$7K@crE(R=Si7tx~k-h1yy zFW+@M?|sMfe*c2c81D}_RHrMo8xRK>2cFOjpgY#Q0x*RqQ?0G?~Ki{-TQIzVJHeP^cx!Rng}8a zirewHv6rS>rZ6)DWeQ!j%k|5=)ITKidnmBP2U1H*d%IA6OceMZ0jYdj7i2r?*Ki)aco!Y(6&%rNW3-a?zdO)$Ne&E?!%%DBt9rI z`mpujaBgqBPh<^T-6FRNB;q13+@%($IQqOe%E#LuWJmapD?q*+&uVNIUl!fJ9NRTd zaetbvo%CMxm5!c;r&VPrJH3Qw2L7Q>FLe@h@bi&-AnT#my%b$h!MlVP=?_@raE)$Q zKCqs(K&yvxeR=jKgq$>YzK{LO%lltvuwSNO<2>8JUwc_46G(M0ZGVI*k}&I=$Dsb3 zVI~?Ef5xEZ&_;V`hp09^LQ5a(nV6GA4jm&umJW6Uu}6Kwo38^<>-H{h9Ql)P^sPD~ 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    Problem 2

    For this problem, consider the HTML document shown below:

    <html>
    -    <head>
    -        <title>Data Science Courses</title>
    -    </head>
    +class="sourceCode html"><html>
    +    <head>
    +        <title>Data Science Courses</title>
    +    </head>
         
    -    <body>
    -        <h1>Welcome to the World of Data Science!</h1>
    +    <body>
    +        <h1>Welcome to the World of Data Science!</h1>
             
    -        <h2>Current Courses</h2>
    +        <h2>Current Courses</h2>
             
    -        <div class="course_list">
    +        <div class="course_list">
             
    -            <img alt="Course Banner", src="courses.png">
    -            <p>
    +            <img alt="Course Banner", src="courses.png">
    +            <p>
                     Here are the courses available to take:
    -            </p>
    -            <ul>
    -                <li>Machine Learning</li>
    -                <li>Design of Experiments</li>
    -                <li>Driving Business Value with DS</li>
    -            </ul> 
    +            </p>
    +            <ul>
    +                <li>Machine Learning</li>
    +                <li>Design of Experiments</li>
    +                <li>Driving Business Value with DS</li>
    +            </ul> 
     
    -            <p>
    -                For last quarter's classes, see <a href="./2021-sp.html">here</a>.
    -            </p>
    +            <p>
    +                For last quarter's classes, see <a href="./2021-sp.html">here</a>.
    +            </p>
                 
    -        </div>
    +        </div>
             
    -        <h2>News</h2>
    +        <h2>News</h2>
             
    -        <div class="news">
    -            <p class="news">
    -                New course on <b>Visualization</b> is launched.
    -                See <a href="https://http.cat/301.png" target="_blank">here</a>
    -            </p>
    -        </div>
    +        <div class="news">
    +            <p class="news">
    +                New course on <b>Visualization</b> is launched.
    +                See <a href="https://http.cat/301.png" target="_blank">here</a>
    +            </p>
    +        </div>
             
    -    </body>
    -</html>
    + </body> +</html>


    Problem 2.1

    How many children does the div node with class diff --git a/docs/fa22-final/index.html b/docs/fa22-final/index.html index df4fb74..798c947 100644 --- a/docs/fa22-final/index.html +++ b/docs/fa22-final/index.html @@ -621,32 +621,32 @@

    Difficulty: ⭐️⭐️

    Problem 3

    The questions below reference the following HTML.

    <html>
    -    <head>
    -        <title>ZOMBO</title>
    -    </head>
    +class="sourceCode html"><html>
    +    <head>
    +        <title>ZOMBO</title>
    +    </head>
     
    -    <body>
    -        <h1>Welcome to Zombo.com</h1>
    -        <div id="greeting">
    -            <ul>
    -                <li>This is Zombo.com, welcome!</li>
    -                <li>This is Zombo.com</li>
    -                <li>Welcome to Zombo.com</li>
    -                <li>You can do anything at Zombo.com -- anything at all!</li>
    -                <li>The only limit is yourself.</li>
    -            </ul>
    -        </div>
    -        <div id="footnotes" class="faded">
    -            <h3>Footnotes</h3>
    +    <body>
    +        <h1>Welcome to Zombo.com</h1>
    +        <div id="greeting">
    +            <ul>
    +                <li>This is Zombo.com, welcome!</li>
    +                <li>This is Zombo.com</li>
    +                <li>Welcome to Zombo.com</li>
    +                <li>You can do anything at Zombo.com -- anything at all!</li>
    +                <li>The only limit is yourself.</li>
    +            </ul>
    +        </div>
    +        <div id="footnotes" class="faded">
    +            <h3>Footnotes</h3>
     
    -            <ol id="footnotes">
    -                <li>Please consider <a href="paypal.html">donating!</a></li>
    -                <li>Made in California with <a href="https://reactj.org">React.</a><li>
    -            </ol>
    -        </div>
    -    </body>
    -</html>
    + <ol id="footnotes"> + <li>Please consider <a href="paypal.html">donating!</a></li> + <li>Made in California with <a href="https://reactj.org">React.</a><li> + </ol> + </div> + </body> +</html>


    Problem 3.1

    Consider the node representing the body tag in the diff --git a/docs/fa23-final/index.html b/docs/fa23-final/index.html index 32037cb..6efbab9 100644 --- a/docs/fa23-final/index.html +++ b/docs/fa23-final/index.html @@ -401,17 +401,18 @@

    Problem 2

    res = x[:-2].split(':') return convert(res[0], res[1] if len(res) == 2 else 0, x[-2:])

    Option B:

    -
    def parse(x):
    -    res = re.match(r'(\d+):(\d+)([apm]{2}', x).groups()
    -    return convert(res[0], res[1], res[2])
    +
    def parse(x):
    +    res = re.match(r'(\d+):(\d+)([apm]{2}', x).groups()
    +    return convert(res[0], res[1], res[2])

    Option C:

    -
    def parse(x):
    -    res = re.match(r'(\d+)(:(\d+))?(am|pm)', x).groups()
    -    return convert(res[0], res[2], res[3])
    +
    def parse(x):
    +    res = re.match(r'(\d+)(:(\d+))?(am|pm)', x).groups()
    +    return convert(res[0], res[2], res[3])

    Option D:

    -
    def parse(x):
    -    res = re.match(r'(.+(.{3})?)(..)', x).groups()
    -    return convert(res[0], res[1], res[2])
    +
    def parse(x):
    +    res = re.match(r'(.+(.{3})?)(..)', x).groups()
    +    return convert(res[0], res[1], res[2])

    diff --git a/docs/index.html b/docs/index.html index 2317107..b203342 100644 --- a/docs/index.html +++ b/docs/index.html @@ -11,8 +11,11 @@ div.columns{display: flex; gap: min(4vw, 1.5em);} div.column{flex: auto; overflow-x: auto;} div.hanging-indent{margin-left: 1.5em; text-indent: -1.5em;} - ul.task-list{list-style: none;} + /* The extra [class] is a hack that increases specificity enough to + override a similar rule in reveal.js */ + ul.task-list[class]{list-style: none;} ul.task-list li input[type="checkbox"] { + font-size: inherit; width: 0.8em; margin: 0 0.8em 0.2em -1.6em; vertical-align: middle; @@ -61,7 +64,6 @@

    especially important that you practice on paper, since your exams will also be on paper. Even though you will see some multiple choice bubbles, you intentionally cannot select them.

    -
    @@ -91,7 +93,8 @@

    Suraj Rampure

    @@ -103,7 +106,7 @@

    @@ -114,7 +117,7 @@

    Tauhidur Rahman

    @@ -126,7 +129,7 @@

    diff --git a/docs/sp22-final/index.html b/docs/sp22-final/index.html index 8802183..a5d006b 100644 --- a/docs/sp22-final/index.html +++ b/docs/sp22-final/index.html @@ -1177,34 +1177,34 @@

    Problem 6

    containing the top few songs with the most streams on Spotify today in Canada.

    <head>
    -    <title>3*Canada-2022-06-04</title>
    -<head>
    -<body>
    -    <h1>Spotify Top 3 - Canada</h1>
    -    <table>
    -        <tr class='heading'>
    -            <th>Rank</th>
    -            <th>Artist(s)</th> 
    -            <th>Song</th>
    -        </tr>
    -        <tr class=1>
    -            <td>1</td>
    -            <td>Harry Styles</td> 
    -            <td>As It Was</td>
    -        </tr>
    -        <tr class=2>
    -            <td>2</td>
    -            <td>Jack Harlow</td> 
    -            <td>First Class</td>
    -        </tr>
    -        <tr class=3>
    -            <td>3</td>
    -            <td>Kendrick Lamar</td> 
    -            <td>N95</td>
    -        </tr>
    -    </table>
    -</body>
    +class="sourceCode html"><head> + <title>3*Canada-2022-06-04</title> +<head> +<body> + <h1>Spotify Top 3 - Canada</h1> + <table> + <tr class='heading'> + <th>Rank</th> + <th>Artist(s)</th> + <th>Song</th> + </tr> + <tr class=1> + <td>1</td> + <td>Harry Styles</td> + <td>As It Was</td> + </tr> + <tr class=2> + <td>2</td> + <td>Jack Harlow</td> + <td>First Class</td> + </tr> + <tr class=3> + <td>3</td> + <td>Kendrick Lamar</td> + <td>N95</td> + </tr> + </table> +</body>

    Suppose we define soup to be a BeautifulSoup object that is instantiated using the document above.

    diff --git a/docs/sp23-final/index.html b/docs/sp23-final/index.html index cedb501..1951094 100644 --- a/docs/sp23-final/index.html +++ b/docs/sp23-final/index.html @@ -11,8 +11,11 @@ div.columns{display: flex; gap: min(4vw, 1.5em);} div.column{flex: auto; overflow-x: auto;} div.hanging-indent{margin-left: 1.5em; text-indent: -1.5em;} - ul.task-list{list-style: none;} + /* The extra [class] is a hack that increases specificity enough to + override a similar rule in reveal.js */ + ul.task-list[class]{list-style: none;} ul.task-list li input[type="checkbox"] { + font-size: inherit; width: 0.8em; margin: 0 0.8em 0.2em -1.6em; vertical-align: middle; @@ -154,7 +157,7 @@

    Click to view the solution.

    -
    @@ -192,7 +195,7 @@

    Click to view the solution.

    -
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    Click to view the solution.

    -
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    Click to view the solution.

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    Click to view the solution.

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    Click to view the solution.

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    Click to view the solution.

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    Click to view the solution.

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    Click to view the solution.

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    Click to view the solution.

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    Click to view the solution.

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    Click to view the solution.

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    Click to view the solution.

    -
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    Click to view the solution.

    -
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    Click to view the solution.

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    Click to view the solution.

    -
    @@ -852,7 +855,7 @@

    Click to view the solution.

    -
    @@ -897,7 +900,7 @@

    Click to view the solution.

    -
    @@ -953,7 +956,7 @@

    Click to view the solution.

    -
    @@ -1001,7 +1004,7 @@

    Click to view the solution.

    -
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    Click to view the solution.

    -
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    Click to view the solution.

    -
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    Click to view the solution.

    -
    @@ -1203,7 +1206,7 @@

    Click to view the solution.

    -
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    Click to view the solution.

    -
    @@ -1292,7 +1295,7 @@

    Click to view the solution.

    -
    @@ -1330,7 +1333,7 @@

    Click to view the solution.

    -
    @@ -1359,7 +1362,7 @@

    Click to view the solution.

    -
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    Click to view the solution.

    -
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    Click to view the solution.

    -
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    Click to view the solution.

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    Click to view the solution.

    -
    @@ -1537,7 +1540,7 @@

    Click to view the solution.

    -
    diff --git a/docs/sp23-midterm/index.html b/docs/sp23-midterm/index.html deleted file mode 100644 index 0c09ac8..0000000 --- a/docs/sp23-midterm/index.html +++ /dev/null @@ -1,180 +0,0 @@ - - - - - - - Spring 2023 Midterm Exam - - - - - - - - -
    -

    Spring 2023 Midterm Exam

    -
    -

    - - - - -

    - - - - - -

    ← return to practice.dsc80.com

    -
    -

    Instructor(s): Tauhidur Rahman

    -

    This exam was administered in-person. The exam was closed-notes, -except students were allowed to bring a single two-sided cheat sheet. No -calculators were allowed. Students had 50 minutes to -take this exam.

    -
    -

    Problem 1

    -

    Consider the following Code Snippet:

    -
    re.findall(r'--(a)--', 
    -           'my cat is hungry, concatenate!, catastrophe! What a cat!')
    -


    -

    Problem 1.1

    -

    Which regular expression in (a) will generate the -following output?

    -
    Output: ['my', 'a'] 
    -

    ( )

    -
    \b([a-z]*)cat\b
    -

    ( )

    -
    \b[a-z]*\scat\b
    -

    ( )

    -
    ([a-z]*)\scat\b
    -

    ( )

    -
    \b([a-z]*\scat)\b
    -
    -
    -

    - -

    -
    -
    -
    -

    -
    -
    -
    -
    -
    -


    -

    Problem 1.2

    -

    Which regular expression in (a) will generate the -following output?

    -
    Output: ['concatenate']
    -

    ( )

    -
    \b.*cat.*\b
    -

    ( )

    -
    [a-z]*cat[a-z]*
    -

    ( )

    -
    [a-z]+cat[a-z]+
    -

    ( )

    -
    \b[a-z]*cat[a-z]*\b
    -
    -
    -

    - -

    -
    -
    -
    -

    -
    -
    -
    -
    -
    -


    -

    Problem 1.3

    -

    Which regular expression in (a) will generate the -following output?

    -
    Output: ['cat', 'concatenate', 'catastrophe', 'cat']
    -

    ( )

    -
    .*cat.*
    -

    ( )

    -
    \b.*cat.*\b
    -

    ( )

    -
    \b[a-z]*cat[a-z]*\b
    -

    ( )

    -
    \b[a-z]+cat[a-z]+\b
    -
    -
    -

    - -

    -
    -
    -
    -

    -
    -
    -
    -
    -
    -


    -
    -

    -

    👋 -Feedback: Find an error? Still confused? Have a suggestion? -Let us know -here.

    -
    - - diff --git a/docs/wi24-final/index.html b/docs/wi24-final/index.html new file mode 100644 index 0000000..3e820bc --- /dev/null +++ b/docs/wi24-final/index.html @@ -0,0 +1,2101 @@ + + + + + + + Winter 2024 Final Exam + + + + + + + + +
    +

    Winter 2024 Final Exam

    +
    +

    + + + + +

    + + + + + +

    ← return to practice.dsc80.com

    +
    +

    Instructor(s): Suraj Rampure

    +

    This exam was administered in-person. The exam was closed-notes, +except students were allowed to bring two two-sided notes sheets. No +calculators were allowed. Students had 180 minutes to +take this exam.

    +
    +

    The DSC 80 staff are looking into hotels — some in San Diego, for +their family to stay at for graduation, and some elsewhere, for summer +trips.

    +

    In Question 1 only, you will work with the DataFrame +hotels. Each row of hotels contains +information about a different hotel in San Diego. Specifically, for each +hotel, we have:

    +
      +
    • "Hotel Name" (str): The name of the hotel. +Assume hotel names are unique.
    • +
    • "Location" (str): The hotel’s neighborhood in San +Diego
    • +
    • "Chain" (str): The chain the hotel is a part of; either +"Hilton", "Marriott", "Hyatt", or "Other". A hotel chain is +a group of hotels owned or operated by a shared company
    • +
    • "Number of Rooms" (int): The number of rooms the hotel +has.
    • +
    +

    The first few rows of hotels are shown below, but hotels +has many more rows than are shown.

    +
    +

    Remember that hotels is only being used in Question 1; +other questions will introduce other assumptions.

    +

    Throughout the exam, assume we have already run the +necessary import statements.

    +
    +

    Problem 1

    +

    Consider the variable summed, defined below.

    +

    summed = hotels.groupby("Chain")["Number of Rooms"].sum().idxmax()

    +


    +

    Problem 1.1

    +

    What is type(summed)?

    +
      +
    • int

    • +
    • str

    • +
    • Series

    • +
    • DataFrame

    • +
    • DataFrameGroupBy

    • +
    +
    +
    +

    + +

    +
    +
    +
    +

    +
    +

    Answer: str

    +

    When we do a groupby on the Chain column in +hotels, this means that the values in the +Chain column will be the indices of the DataFrame or Series +we get as output, in this case the Series +hotels.groupby("Chain")["Number of Rooms"].sum().

    +

    Since the values of Chain are strings, and since +.idxmax() will return a value from the index of the +aforementioned Series, summed is a string.

    +
    +
    Difficulty: ⭐️⭐️
    +

    +

    The average score on this problem was 88%.

    +

    +
    +
    +
    +
    +


    +

    Problem 1.2

    +

    In one sentence, explain what the value of summed means. +Phrase your explanation as if you had to give it to someone who is not a +data science major; that is, don’t say something like “it is the result +of grouping hotels by "Chain", selecting the +"Number of Rooms" column, …”, but instead, give the value +context.

    +
    +
    +

    + +

    +
    +
    +
    +

    +
    +

    Answer: summed is the name of the hotel +chain with the most total rooms

    +

    The result of the .groupby() and .sum() is +a Series indexed by the unique Chains, whose values are the +total number of rooms in hotels owned by each chain. The +idxmax() function gets the index corresponding to the +largest value in the Series, which will be the hotel chain name with the +most total rooms.

    +
    +
    Difficulty: ⭐️
    +

    +

    The average score on this problem was 97%.

    +

    +
    +
    +
    +
    +


    +

    Problem 1.3

    +

    Consider the variable curious, defined below.

    +

    curious = frame["Chain"].value_counts().idxmax()

    +

    Fill in the blank: curious is guaranteed to be equal to +summed only if frame has one row for every +____ in San Diego.

    +
      +
    • hotel

    • +
    • hotel chain

    • +
    • hotel room

    • +
    • neighborhood

    • +
    +
    +
    +

    + +

    +
    +
    +
    +

    +
    +

    Answer: hotel room

    +

    curious gets the most common value of Chain +in the DataFrame frame. We already know that +summed is the hotel chain with the most rooms in San Diego, +so curious only equals summed if the most +common Chain in frame is the hotel chain with +the most total rooms; this occurs when each row of frame is +a single hotel room.

    +
    +
    Difficulty: ⭐️⭐️
    +

    +

    The average score on this problem was 80%.

    +

    +
    +
    +
    +
    +


    +

    Problem 1.4

    +

    Fill in the blanks so that popular_areas is an array of +the names of the unique neighborhoods that have at least 5 hotels and at +least 1000 hotel rooms.

    +
        f = lambda df: __(i)__
    +    popular_areas = hotels.groupby(__(ii)__).__(iii)__.__(iv)__
    +
      +
    1. What goes in blank (i)?

    2. +
    3. What goes in blank (ii)?

    4. +
    +
      +
    • "Hotel Name"

    • +
    • "Location"

    • +
    • "Chain"

    • +
    • "Number of Rooms"

    • +
    +
      +
    1. What goes in blank (iii)?
    2. +
    +
      +
    • agg(f)

    • +
    • filter(f)

    • +
    • transform(f)

    • +
    +
      +
    1. What goes in blank (iv)?
    2. +
    +
    +
    +

    + +

    +
    +
    +
    +

    +
    +

    Answers:

    +
      +
    1. df.shape[0] >= 5 and df["Number of Rooms"].sum() >= 1000
    2. +
    3. "Location"
    4. +
    5. filter(f)
    6. +
    7. ["Location"].unique() or equivalent
    8. +
    +

    We’d like to only consider certain neighborhoods according to group +characteristics (having >= 5 hotels and >= 1000 hotel rooms), and +.filter() allows us to do that by excluding groups not +meeting those criteria. So, we can write a function that evaluates those +criteria on one group at a time (the df of input to +f is the subset of hotels containing just one +Location value), and calling filter(f) means +that the only remaining rows are hotels in neighborhoods that match +those criteria. Finally, all we have to do is get the unique +neighborhoods from this DataFrame, which are the neighborhoods for which +f returned True.

    +
    +
    Difficulty: ⭐️⭐️
    +

    +

    The average score on this problem was 83%.

    +

    +
    +
    +
    +
    +


    +

    Problem 1.5

    +

    Consider the code below.

    +
        cond1 = hotels["Chain"] == "Marriott"
    +    cond2 = hotels["Location"] == "Coronado"
    +    combined = hotels[cond1].merge(hotels[cond2], on="Hotel Name", how=???)
    +
      +
    1. If we replace ??? with "inner" in the +code above, which of the following will be equal to +combined.shape[0]?

    2. +
    3. If we replace ??? with "outer" in the +code above, which of the following will be equal to +combined.shape[0]?

    4. +
    +
    +
    +

    + +

    +
    +
    +
    +

    +
    +

    Answers:

    +
      +
    1. (cond1 & cond2).sum()
    2. +
    3. cond1.sum() + cond2.sum() - (cond1 & cond2).sum()
    4. +
    +

    Note that cond1 and cond2 are boolean +Series, and hotels[cond1] and hotels[cond2] +are the subsets of hotels where +Chain == "Marriott and +"Location" == "Coronado", respectively.

    +
      +
    1. When we perform an inner merge, we’re selecting every row where a +Hotel Name appears in both +hotels[cond1] and hotels[cond2]. This is the +same set of indices (and therefore hotel names, since those are unique) +as where (cond1 & cond2) == True. So, the length of +combined will be the same as the number of +Trues in (cond1 & cond2).

    2. +
    3. When we perform an outer merge, we’re selecting every row that +appears in either DataFrame, although there will not be repeats +for hotels that are both Marriott properties and are in Coronado. So, to +find the total number of rows in either DataFrame, we take the sum of +the sizes of each, and subtract rows that appear in both, which +corresponds to answer +cond1.sum() + cond2.sum() - (cond1 & cond2).sum().

    4. +
    +
    +
    Difficulty: ⭐️⭐️
    +

    +

    The average score on this problem was 79%.

    +

    +
    +
    +
    +
    +


    +
    +

    Problem 2

    +

    At the Estancia La Jolla, the hotel manager enters information about +each reservation in the DataFrame guests, after guests +check into their rooms. Specifically, guests has the +columns:

    +
      +
    • "id" (str): The booking ID +(e.g. "SN1459").
    • +
    • "age" (int): The age of the primary occupant (the +person who made the reservation).
    • +
    • "people" (int): The total number of occupants.
    • +
    • "is_business" (str): Whether or not the trip is a +business trip for the primary occupant (possible values: +"yes", "no", and +"partially").
    • +
    • "company" (str): The company that the primary occupant +works for, if this is a business trip.
    • +
    • "loyalty" (int): The loyalty number of the primary +occupant. Note that most business travelers have a loyalty number.
    • +
    +

    Some of the values in guests are missing.

    +


    +

    Problem 2.1

    +

    What is the most likely missingness mechanism of the +"loyalty" column?

    +
      +
    • Missing by design

    • +
    • Missing at random

    • +
    • Not missing at random

    • +
    • Missing completely at random

    • +
    +
    +
    +

    + +

    +
    +
    +
    +

    +
    +

    Answer: missing at random

    +

    The description of loyalty indicates that most business +travelers have a loyalty number – in other words, that depending on the +value of is_business, the probability of a present value +for loyalty can increase or decrease. This is therefore an +example of MAR.

    +
    +
    Difficulty: ⭐️⭐️⭐️
    +

    +

    The average score on this problem was 67%.

    +

    +
    +
    +
    +
    +


    +

    Problem 2.2

    +

    What is the most likely missingness mechanism of the +"company" column?

    +
      +
    • Missing by design

    • +
    • Missing at random

    • +
    • Not missing at random

    • +
    • Missing completely at random

    • +
    +
    +
    +

    + +

    +
    +
    +
    +

    +
    +

    Answer: missing by design

    +

    The value of company is missing if the trip is a +business trip, and since this relationship should be deterministic, then +this column is missing by design.

    +
    +
    Difficulty: ⭐️⭐️⭐️
    +

    +

    The average score on this problem was 60%.

    +

    +
    +
    +
    +
    +


    +

    Problem 2.3

    +

    Fill in the blanks: To assess whether the missingness of +"is_business" depends on "age", we should +perform a __(i)__ with __(ii)__ as the test +statistic.

    +
      +
    1. What goes in blank (i)?
    2. +
    +
      +
    • standard hypothesis test

    • +
    • permutation test

    • +
    +
      +
    1. What goes in blank (ii)?
    2. +
    +
      +
    • the total variation distance

    • +
    • the sample mean

    • +
    • the (absolute) difference in means

    • +
    • the K-S statistic

    • +
    • either the (absolute) difference in means or the K-S statistic, +depending on the shapes of the observed distributions

    • +
    +
    +
    +

    + +

    +
    +
    +
    +

    +
    +

    Answers: 1. permutation test 2. either the +(absolute) difference in means or the K-S statistic, depending on the +shapes of the observed distributions

    +

    In part 1, we use a permutation test because we’re comparing two +sampled distributions (the values of age for rows with +missing vs. present values of is_business), rather than +comparing our sample distribution to a known population +distribution/metric.

    +

    For part 2, we should note that the test statistic, for each +iteration of our permutation test, is meant to compare two distributions +of the variable age, which is continuous. TVD is not +well-suited for this, since it compares discrete, categorical +distributions, and neither is “sample mean,” since we have two samples +to compare. Differences in means or the K-S statistic work because they +both compare two continuous distributions. However, there are cases in +which the difference in means might not capture differences in +distributions (for example, two distributions with the same mean but +very different standard deviation); this is the reason for the caveat in +the correct solution.

    +
    +
    Difficulty: ⭐️⭐️⭐️
    +

    +

    The average score on this problem was 68%.

    +

    +
    +
    +
    +
    +


    +

    Problem 2.4

    +

    Fill in the blanks: To assess whether the missingness of +"age" depends on "is business", we should +perform a __(i)__ with __(ii)__ as the test +statistic.

    +
      +
    1. What goes in blank (i)?
    2. +
    +
      +
    • standard hypothesis test

    • +
    • permutation test

    • +
    +
      +
    1. What goes in blank (ii)?
    2. +
    +
      +
    • the total variation distance

    • +
    • the sample mean

    • +
    • the (absolute) difference in means

    • +
    • the K-S statistic

    • +
    • either the (absolute) difference in means or the K-S statistic, +depending on the shapes of the observed distributions

    • +
    +
    +
    +

    + +

    +
    +
    +
    +

    +
    +

    Answers:

    +
      +
    1. permutation test
    2. +
    3. total variation distance
    4. +
    +

    For part 1, the reasoning is the same as the previous part – the only +difference is that now, we’re comparing two categorical distributions +rather than two continuous ones.

    +

    In part 2, we can note that we’re now comparing the categorical +distributions of is_business, which can only have values of +"yes", "no", and "partially", for +rows with missing vs. present values of age. (Even though +age is continuous, since we’re only using whether or not +age is missing and not the actual values in the column, +this doesn’t really matter.) The only test statistic listed that is +meant to compare two categorical distributions is TVD, so this is the +correct solution.

    +
    +
    Difficulty: ⭐️⭐️⭐️
    +

    +

    The average score on this problem was 72%.

    +

    +
    +
    +
    +
    +


    +

    Problem 2.5

    +

    After running the code below, p is equal to the +simulated p-value for a statistical test.

    +
        obs = guests.groupby("is_business")["age"].median().loc["no"]
    +    p = 0
    +    for _ in range(10000):
    +        s = guests.sample((guests["is_business"] == "no").sum(),
    +        replace=False)
    +        sm = s["age"].median()
    +        p += (obs >= sm) / 10000
    +
      +
    1. What type of test is this?
    2. +
    +
      +
    • standard hypothesis test

    • +
    • permutation test

    • +
    +

    Fill in the blanks: The alternative hypothesis being tested above is +that the median age of primary occupants not on a +business trip is __(ii)__ the median age of +__(iii)__.

    +
      +
    1. What goes in blank (ii)?
    2. +
    +
      +
    • greater than or equal to

    • +
    • greater than

    • +
    • equal to

    • +
    • not equal to

    • +
    • less than or equal to

    • +
    • less than

    • +
    +
      +
    1. What goes in blank (iii)?
    2. +
    +
      +
    • all primary occupants

    • +
    • primary occupants at least partially on a business trip (that is, +primary occupants who have an "is_business" value of +"yes" or "partially")

    • +
    +
    +
    +

    + +

    +
    +
    +
    +

    +
    +

    Answers:

    +
      +
    1. standard hypothesis test
    2. +
    3. less than
    4. +
    5. all primary occupants
    6. +
    +

    For part 1, this is a standard hypothesis test, because instead of +shuffling the values of a particular column, we are sampling entire rows +of the DataFrame; the size of these samples is the same as the number of +guests who are not (even partially) on business trips. By sampling +randomly from the entire DataFrame, this assumes the null hypothesis +that the distribution of age of primary occupants not on a +business trip is equal to the distribution of age for occupants as a +whole. Therefore, this procedure is meant to simulate values of the +median age of a sample of size +guests["is_business"] == "no").sum(), and sampling random +rows means that we’re assuming that is_business == "no" and +age are unrelated.

    +

    For part 2, the samples capture how likely the deviation of the +observed statistic is to happen under the null hypothesis, but the +p-value is being calculated by adding up whenever the observed statistic +is greater or equal to the sample. This indicates that we’re doing a +one-tailed test, and since to reject the null hypothesis and provide +some evidence towards the alternate hypothesis, the p-value should be +lower, the alternate hypothesis should be the complement of +obs >= sum.

    +

    For part 3, the answer is “all primary occupants” because our +sampling procedure doesn’t sample just from (full or partial) business +travelers, but from the entire DataFrame. (In the line where we sample, +the only arguments are the number of rows we’re sampling, and that we’re +doing so without replacement – nothing about restricting which rows in +guest to sample.) In other words, we’re not comparing +primary occupants not on business trips to those on business trips, but +rather we’re comparing primary occupants to the entire dataset of +occupants.

    +
    +
    Difficulty: ⭐️⭐️⭐️
    +

    +

    The average score on this problem was 58%.

    +

    +
    +
    +
    +
    +


    +
    +

    Problem 3

    +

    Weiyue proposes the following imputation scheme.

    +
        def impute(s):
    +        return s.fillna(np.random.choice(s[s.notna()]))
    +


    +

    Problem 3.1

    +

    True or False: impute performs +probabilistic imputation, using the same definition of probabilistic +imputation we learned about in class.

    +
      +
    • True

    • +
    • False

    • +
    +
    +
    +

    + +

    +
    +
    +
    +

    +
    +

    Answer: False

    +

    In impute, np.random.choice will return a +single non-null value from s, and .fillna() +will fill every null value with this single value. Meanwhile, +probabilistic imputation draws a different value from a specified +distribution to fill each missing value, making it such that there won’t +be a single “spike” in the imputed distribution at a single chosen +value.

    +
    +
    Difficulty: ⭐️⭐️⭐️⭐️
    +

    +

    The average score on this problem was 41%.

    +

    +
    +
    +
    +
    +


    +

    Problem 3.2

    +

    Consider the following expressions and values.

    +
        >>> vals.isna().mean()
    +    0.2
    +    >>> vals.describe().loc[["min", "mean", "max"]]
    +    min     2.0
    +    mean    4.0
    +    max     7.0
    +    dtype: float64
    +

    Given the above, what is the maximum possible value +of impute(vals).mean()? Give your answer as a number +rounded to one decimal place.

    +
    +
    +

    + +

    +
    +
    +
    +

    +
    +

    Answer: 4.6

    +

    The maximum possible value of impute(vals).mean() would +occur when every single missing value in vals is filled in +with the highest possible non-null value in vals. (As +discussed in the previous solution, impute selects only one +value from s to fill into every missing space.)

    +

    If this occurs, then the mean of the imputed Series will be weighted +mean of the available data and the filled data, and given the numbers in +the question, this is 0.8 \cdot 4 + 0.2 \cdot +7, or 4.6.

    +
    +
    Difficulty: ⭐️⭐️⭐️
    +

    +

    The average score on this problem was 50%.

    +

    +
    +
    +
    +
    +


    +

    Problem 3.3

    +

    Which of the following statements below will always evaluate to +True?

    +
      +
    • vals.std() < impute(vals).std()

    • +
    • vals.std() <= impute(vals).std()

    • +
    • vals.std() == impute(vals).std()

    • +
    • vals.std() >= impute(vals).std()

    • +
    • vals.std() > impute(vals).std()

    • +
    • None of the above

    • +
    +
    +
    +

    + +

    +
    +
    +
    +

    +
    +

    Answer: None of the above

    +

    Since the value which impute() will choose to impute +with is random, the effect that it has on the standard deviation of +vals is unknown. If the missing values are filled with a +value close to the mean, this could reduce standard deviation; if they +are filled with a value far from the mean, this could increase standard +deviation. (Of course, the imputation will also shift the mean, so +without knowing details of the Series, it’s impossible to come up with +thresholds.) In any case, since the value for imputation is chosen at +random, none of these statements will always be true, and so +the correct answer is “none of the above.”

    +
    +
    Difficulty: ⭐️⭐️⭐️⭐️
    +

    +

    The average score on this problem was 38%.

    +

    +
    +
    +
    +
    +


    +
    +

    Problem 4

    +

    Suppose site is a BeautifulSoup object +instantiated on the HTML document below.

    +
    <html>
    +    <div align="center">
    +        <h3>Luxury Hotels in Bali from May 2-6, 2024 for Ethan</h3>
    +        <div class="chain" name="Hilton">
    +            <h3 style="color: blue">Hilton Properties in Bali</h3>
    +        </div>
    +        <div class="chain" name="Marriott">
    +            <h3 style="color: red">Marriott Properties in Bali</h3>
    +        </div>
    +        <div __(i)__>
    +            __(ii)__
    +        </div>
    +    </div>
    +</html>
    +


    +

    Problem 4.1

    +

    What does len(site.find_all("div")) evaluate to? Give +your answer as an integer. For this part only, assume that both blank +(i) and blank (ii) are left blank.

    +
    +
    +

    + +

    +
    +
    +
    +

    +
    +

    Answer: 4

    +

    The answer simply requires counting the number of div +elements, making sure not to double-count opening and closing tags.

    +
    +
    Difficulty: ⭐️⭐️
    +

    +

    The average score on this problem was 82%.

    +

    +
    +
    +
    +
    +


    +

    Problem 4.2

    +

    Fill in the blank so that chain_color takes in the name +of a hotel chain and returns the color used to display the hotel chain +in site. For example, chain_color("Hilton") should return +"blue" and chain_color("Marriott") should +return "red".

    +
    chain_color = lambda chain: site.____.split()[-1]
    +
    +
    +

    + +

    +
    +
    +
    +

    +
    +

    Answer: +find("div", attrs={"name": chain}).find("h3").get("style")

    +

    The solution finds all div elements whose +name attribute is equal to the function input +chain (which is how the chains are defined in the HTML +document). Then, the colors are stored as part of the style +attribute in an h3 tag within that div, so we +find the first – and in this document, only – h3 tag within +the div and get its style attribute. This +returns a string like color: red, from which the given code +.split()[-1] returns the last word, which is the correct +color.

    +
    +
    Difficulty: ⭐️⭐️⭐️
    +

    +

    The average score on this problem was 67%.

    +

    +
    +
    +
    +
    +


    +

    Problem 4.3

    +

    Fill in blanks (i) and (ii) in site so that the +following all evaluate to True:

    +
      +
    • len(site.find all("div", class ="chain")) == 2
    • +
    • chain_color("Hyatt") == "purple"
    • +
    • site.find all("div")[-1].text == ""
    • +
    +
      +
    1. What goes in blank (i)?
    2. +
    3. What goes in blank (ii)?
    4. +
    +
    +
    +

    + +

    +
    +
    +
    +

    +
    +

    Answers:

    +
      +
    1. name = "Hyatt"
    2. +
    3. <h3 style="color: purple"></h3>
    4. +
    +

    In order to make all of the three given statements true, we need to +make it such that there are 2 div elements with class +chain, the chain_color function returns +purple for Hyatt, and the last +div tag in the document has no text.

    +

    We do this by defining a div similar to the previous +two, but without the chain class (because there are already +2 in the document). In order for chain_color("Hyatt") to +return purple, we add "Hyatt" as a +name attribute in the div, and add an +h3 tag within that div with +style="color: purple". However, since the last statement +requires the last div in the document has no text, and the +div we’re currently making will be the final one, we don’t +include any text in the h3 tag. (Note that because the +chain_color function doesn’t use the hotel name in the text +to find a given chain’s name, but rather the name attribute in the +enclosing div tag.)

    +
    +
    Difficulty: ⭐️
    +

    +

    The average score on this problem was 90%.

    +

    +
    +
    +
    +
    +


    +
    +

    Problem 5

    +

    Dylan finds a messy text file containing room availability and +pricing information at his favorite local hotel, the Manchester Grand +Hyatt.

    +


    +

    Problem 5.1

    +

    Availability strings are formatted like so:

    +
        avail = """Standard: Available, This23: Available,
    +    Suite: Available, Economy: Not Available,
    +    Rooms are Available, Deluxe: Available"""
    +

    Fill in the blank below so that exp1 is a regular +expression such that if s is an availability string in the +format above, re.findall(exp1, s) will return a list of all +of the available room categories in s. Example behavior is +given below.

    +
        >>> re.findall(exp1, avail)
    +    ["Standard", "Suite", "Deluxe"] # Categories don't include numbers
    +

    Note that your answer needs to work on other availability strings; +you should not hard-code "Standard", "Suite", +or "Deluxe".

    +
    exp1 = r"_____________"
    +
    +
    +

    + +

    +
    +
    +
    +

    +
    +

    Answer: ([A-Za-z]+): Available

    +

    In the above availability strings, we’re looking for a +one-or-more-length sequence of letters (not numbers, as mentioned in the +problem), followed by a colon and the word “Available.” However, since +we only want to return the room type, and not the colon or the word +“Available,” we use a capturing group (the parentheses) to just return +the word before the colon.

    +
    +
    Difficulty: ⭐️⭐️⭐️
    +

    +

    The average score on this problem was 57%.

    +

    +
    +
    +
    +
    +


    +

    Problem 5.2

    +

    Consider the string prices, defined below.

    +
        one = "Standard room: $120, $2.Deluxe room: $200.75"
    +    two = "Other: 402.99, Suite: $350.25"
    +    prices = one + ", " + two
    +
      +
    1. What does re.findall(r"\$\d+\.\d{2}$", prices) evaluate +to?
    2. +
    +
      +
    • ["$200.75", "$402.99", "$350.25"]

    • +
    • ["200.75", "402.99", "350.25"]

    • +
    • ["$120", "$200.75", "$350.25"]

    • +
    • ["$350.25"]

    • +
    • ["$200.75", "$350.25"]

    • +
    +
      +
    1. What does re.findall(r"\$?(\d+\.\d{2})", prices) +evaluate to?
    2. +
    +
      +
    • ["$200.75", "$402.99", "$350.25"]

    • +
    • ["200.75", "402.99", "350.25"]

    • +
    • ["$120", "$200.75", "$350.25"]

    • +
    • ["$350.25"]

    • +
    • ["$200.75", "$350.25"]

    • +
    +
    +
    +

    + +

    +
    +
    +
    +

    +
    +

    Answers:

    +
      +
    1. ["$350.25"]
    2. +
    3. ["200.75", "402.99", "350.25"]
    4. +
    +

    In the first part, the string that the pattern matches is a dollar +sign ($), one or more digits (\d+), a period +(\.), two digits (\d{2}), followed by the end +of the string ($). Since the string we’re passing into +re.findall is prices, which is the +concatenation of one + ", " + two, the only option that +matches is the last price displayed, "$350.25". (If we had +not specified the match ending with the end of the string, +"$200.75" would also have been a match.)

    +

    In the second part, the beginning of the pattern is +"\$?", which means to match zero or one instance +of the dollar sign character. In most cases, this means that if there is +a dollar sign before the remainder of the pattern, it will be included +in the match, but if not, the rest of the pattern will still match. +However, the capturing group around the remainder of the pattern means +that in either case, only the remainder of the pattern after the dollar +sign is captured. (So, in this particular example, the \$? +has no effect on the output.)

    +

    The rest of the pattern is structured similarly to the previous part, +except now, the pattern does not require the end of the string after the +price, so we’re just selecting sequences of digits followed by a period +and two more digits, which is how we get our solution.

    +
    +
    Difficulty: ⭐️⭐️⭐️
    +

    +

    The average score on this problem was 65%.

    +

    +
    +
    +
    +
    +


    +
    +

    Problem 6

    +

    Gabriel decides to look at reviews for the Catamaran Resort Hotel and +Spa. TripAdvisor has 96 reviews for the hotel; of those 96, Gabriel’s +favorite review was:

    +
        "close to the beach but far from the beach beach"
    +


    +

    Problem 6.1

    +

    What is the TF of "beach" in Gabriel’s favorite review? +Give your answer as a simplified fraction.

    +
    +
    +

    + +

    +
    +
    +
    +

    +
    +

    Answer: \frac{3}{10}

    +

    The answer is simply the proportion of words in the sentence that are +the word "beach". There are 10 words in the sentence, 3 of +which are "beach".

    +
    +
    Difficulty: ⭐️
    +

    +

    The average score on this problem was 97%.

    +

    +
    +
    +
    +
    +


    +

    Problem 6.2

    +

    The TF-IDF of "beach" in Gabriel’s favorite review is +\frac{9}{10}, when using a base-2 +logarithm to compute the IDF. How many of the reviews on TripAdvisor for +this hotel contain the term "beach"?

    +
    +
    +

    + +

    +
    +
    +
    +

    +
    +

    Answer: 12

    +

    The TF-IDF is the product of the TF and IDF terms. So if the TF-IDF +of this document is \frac{9}{10}, and +the TF is \frac{3}{10}, as established +in the last part, the IDF of the term "beach" is 3. The IDF +for a word is the log of the inverse of the proportion of documents in +which the word appears. So, since we know there are 96 total +documents.

    +

    3 = log_{2}(\frac{96}{\text{\# documents +containing "beach"}})

    +

    2^{3} = \frac{96}{\text{\# documents +containing "beach"}}

    +

    \boxed{12} = {\text{\# documents +containing "beach"}}

    +
    +
    Difficulty: ⭐️⭐️
    +

    +

    The average score on this problem was 76%.

    +

    +
    +
    +
    +
    +


    +
    +

    Problem 7

    +

    Tiffany decides to look at reviews for the same hotel, but she +modifies them so that the only terms they contain are +"taco" and "sand". The bag-of-words +representations of three reviews are shown as vectors below.

    +
    +

    Using cosine similarity to measure similarity, which pair of reviews +are the most similar? If there are multiple pairs of reviews that are +most similar, select them all.

    +
      +
    • \vec{r}_1 and \vec{r}_2

    • +
    • \vec{r}_1 and \vec{r}_3

    • +
    • \vec{r}_2 and \vec{r}_3

    • +
    +
    +
    +

    + +

    +
    +
    +
    +

    +
    +

    Answer: \vec{r}_1 +and \vec{r}_2, and +\vec{r}_2 and \vec{r}_3

    +

    The cosine similarity of two vectors \vec{a} and \vec{b} is \frac{\vec{a} \cdot \vec{b}}{||\vec{a}|| \cdot +||\vec{b}||}.

    +

    The cosine similarity of \vec{r}_1 +and \vec{r}_2 is:

    +

    \frac{2 \cdot 4 + 3 \cdot 4}{\sqrt{13} +\cdot \sqrt{32}} = \frac{20}{4 \cdot \sqrt{26}} = +\frac{5}{\sqrt{26}}

    +

    The cosine similarity of \vec{r}_1 +and \vec{r}_3 is:

    +

    \frac{2 \cdot 6 + 3 \cdot 4}{\sqrt{13} +\cdot \sqrt{52}} = \frac{24}{26} = \frac{12}{13}

    +

    The cosine similarity of \vec{r}_2 +and \vec{r}_3 is:

    +

    \frac{4 \cdot 6 + 4 \cdot 4}{\sqrt{32} +\cdot \sqrt{52}} = \frac{40}{8 \cdot \sqrt{26}} = +\frac{5}{\sqrt{26}}

    +

    \frac{12}{13} \approx 0.9231, and +\frac{5}{\sqrt{26}} \approx 0.9806, so +our answer is vector pairs \vec{r}_1 +and \vec{r}_2, and \vec{r}_2 and \vec{r}_3

    +
    +
    Difficulty: ⭐️⭐️⭐️
    +

    +

    The average score on this problem was 74%.

    +

    +
    +
    +
    +
    +
    +

    Problem 8

    +

    Consider the corpus of length 13 below, made up of 6 As, 4 Bs, 1 C, +and 2 Rs (and no other tokens). Here, each individual character is +treated as its own token.

    +

    \text{ABABRACABABRA}

    +

    Let P be a function that computes +the probability of the input sequence using a bigram model trained on +the above corpus. For example, P(BR) is +the probability of the sequence BR, using a bigram language model +trained on the above corpus.

    +


    +

    Problem 8.1

    +

    What is P(ABRA)? Give your answer as +a simplified fraction.

    +
    +
    +

    + +

    +
    +
    +
    +

    +
    +

    Answer: \frac{12}{65}

    +

    Using a bigram model, we find the probability of the first token, +then for each remaining token, find its probability given just the +previous token. The probability P(\text{X} | +\text{Y}) is simply the proportion of times that token X is the +next token after the previous token Y. So, for this corpus and input +sequence, we have:

    +

    P(\text{A}) = \frac{6}{13}

    +

    P(\text{B} | \text{A}) = +\frac{4}{5}

    +

    P(\text{R} | \text{B}) = \frac{2}{4} = +\frac{1}{2}

    +

    P(\text{A} | \text{R}) = \frac{2}{2} = +1

    +

    So, we just have to multiply these probabilities together, and we get +\frac{12}{65}.

    +

    Note that the denominator for P(\text{B} | +\text{A}) is 5, not 6, even though there are 6 occurrences of the +letter A. This is because the final one occurs at the end of the +sentence, and we’re not using a stop token or anything else designating +the end of the sequence. So there are only 5 instances of “A” where we +have a subsequent token, which is how we make our probability model.

    +
    +
    Difficulty: ⭐️⭐️⭐️⭐️
    +

    +

    The average score on this problem was 47%.

    +

    +
    +
    +
    +
    +


    +

    Problem 8.2

    +

    Suppose n is a positive integer. Let +[AB]^{n} be the result of repeating the +sequence AB n times. For example, [AB]^{4} is ABABABAB and [AB]^{5} is ABABABABAB.

    +

    Then, it is always the case that:

    +

    P([AB]^{n}) = 2p +(\frac{c}{d})^{k}

    +

    where:

    +
      +
    • p = P(ABRA) is your answer to part +(a)
    • +
    • c and d are positive integers that don’t depend on +n, and \frac{c}{d} is a simplified fraction
    • +
    • k is a positive number that does +depend on n
    • +
    +
      +
    1. What is c? Give your answer as a +positive integer. Remember, your answer should not depend on +n, meaning that it should have no +variables in it.
    2. +
    3. What is d? Give your answer as a +positive integer. Remember, your answer should not depend on +n, meaning that it should have no +variables in it.
    4. +
    5. What is k?
    6. +
    +
      +
    • 2

    • +
    • \frac{n}{2} - 1

    • +
    • \frac{n}{2}

    • +
    • n - 1

    • +
    • n

    • +
    • n + 1

    • +
    +

    Hint: Start by finding P(AB), P(ABAB), and P(ABABAB).

    +
    +
    +

    + +

    +
    +
    +
    +

    +
    +

    Answer:

    +
      +
    1. c = 2
    2. +
    3. d = 5
    4. +
    5. k = n-1
    6. +
    +

    From our work on the previous question, we can see that 2p is equal to P(\text{A}) \cdot P(\text{B} | \text{A}), or +in other words, the probability of the sequence AB.

    +

    The probability of sequence ABAB will be the probability of sequence +AB, times P(\text{A} | \text{B}) \cdot +P(\text{B} | \text{A}). More generally, we can see that after the +first pair of tokens AB (which has a different probability since the +first token is the first in the sequence, and therefore isn’t +conditioned on B), each repetition of AB multiplies a probability of +P(\text{A} | \text{B}) \cdot P(\text{B} | +\text{A}).

    +

    Therefore, our resulting fraction \frac{c}{d} is simply this probability P(\text{A} | \text{B}) \cdot P(\text{B} | +\text{A}). P(\text{A} | +\text{B}) is \frac{1}{2}, and we +already found that P(\text{B} | +\text{A}) is \frac{4}{5}, so the +resulting fraction is \frac{2}{5}. So +c = 2, and d = 5.

    +

    This fraction is multiplied once for each repetition of AB after +the first one (which has a different probability, represented by +2p), and so the exponent should be +n-1.

    +
    +
    Difficulty: ⭐️⭐️⭐️
    +

    +

    The average score on this problem was 66%.

    +

    +
    +
    +
    +
    +


    +
    +

    Problem 9

    +

    Suppose Yutian builds a classifier that predicts whether or not a +hotel provides free parking. The confusion matrix for her classifier, +when evaluated on our training set, is given below.

    +
    +


    +

    Problem 9.1

    +

    What is the precision of Yutian’s classifier? Give your answer as a +simplified fraction.

    +
    +
    +

    + +

    +
    +
    +
    +

    +
    +

    Answer: \frac{8}{13}

    +

    Precision is the proportion of predicted positives that actually were +positives. So, given this confusion matrix, that value is \frac{8}{8 + 5}, or \frac{8}{13}.

    +
    +
    Difficulty: ⭐️⭐️
    +

    +

    The average score on this problem was 89%.

    +

    +
    +
    +
    +
    +


    +

    Problem 9.2

    +

    Fill in the blanks: In order for Yutian’s classifier’s recall to be +equal to its precision, __(i)__ must be equal to +__(ii)__.

    +
      +
    1. What goes in blank (i)?
    2. +
    +
      +
    • A

    • +
    • B

    • +
    +
      +
    1. What goes in blank (ii)?
    2. +
    +
      +
    • 2

    • +
    • 3

    • +
    • 4

    • +
    • 5

    • +
    • 6

    • +
    • 8

    • +
    • 13

    • +
    • 14

    • +
    • 20

    • +
    • 40

    • +
    • 50

    • +
    • 80

    • +
    +
    +
    +

    + +

    +
    +
    +
    +

    +
    +

    Answer:

    +
      +
    1. B
    2. +
    3. 5
    4. +
    +

    We already know that the precision is \frac{8}{13}. Recall is the proportion of +true positives that were indeed classified positives, which in this +matrix is \frac{8}{B + 8}. So, in order +for precision to equal recall, B must +be 5.

    +
    +
    Difficulty: ⭐️
    +

    +

    The average score on this problem was 96%.

    +

    +
    +
    +
    +
    +


    +

    Problem 9.3

    +

    Now, suppose both A and B are unknown. Fill in the blanks: In order +for Yutian’s classifier’s recall to be equal to its accuracy, +__(i)__ must be equal to __(ii)__.

    +
      +
    1. What goes in blank (i)?
    2. +
    +
      +
    • A + B

    • +
    • A - B

    • +
    • B - A

    • +
    • A \cdot B

    • +
    • \frac{A}{B}

    • +
    • \frac{B}{A}

    • +
    +
      +
    1. What goes in blank (ii)?
    2. +
    +
      +
    • 2

    • +
    • 3

    • +
    • 4

    • +
    • 5

    • +
    • 6

    • +
    • 8

    • +
    • 13

    • +
    • 14

    • +
    • 20

    • +
    • 40

    • +
    • 50

    • +
    • 80

    • +
    +

    Hint: To verify your answer, pick an arbitrary value of A, like A += 10, and solve for the B that sets the model’s recall equal to its +accuracy. Do the specific A and B you find satisfy your answer +above?

    +
    +
    +

    + +

    +
    +
    +
    +

    +
    +

    Answer:

    +
      +
    1. A \cdot B
    2. +
    3. 40
    4. +
    +

    We can solve this problem by simply stating recall and accuracy in +terms of the values in the confusion matrix. As we already found, recall +is \frac{8}{B+8}. Accuracy is the sum +of correct predictions over total number of predictions, or \frac{A + 8}{A + B + 13}. Then, we simply set +these equal to each other, and solve.

    +

    \frac{8}{B+8} = \frac{A + 8}{A + B + +13} 8(A + B + 13) = (A + 8)(B + +8) 8A + 8B + 104 = AB + 8A + 8B + +64 104 = AB + 64 AB = 40

    +
    +
    Difficulty: ⭐️⭐️
    +

    +

    The average score on this problem was 79%.

    +

    +
    +
    +
    +
    +


    +
    +

    Problem 10

    +

    Harshi is trying to build a decision tree that predicts whether or +not a hotel has a swimming pool.

    +

    Suppose + represents the “has pool” +class and \circ represents the “no +pool” class. One of the nodes in Harshi’s decision tree has 12 points, +with the following distribution of classes.

    +

    ++++\circ\circ\circ\circ\circ\circ\circ\,\circ

    +

    Consider the following three splits of the node above.

    +

    Split 1:

    +
      +
    • Yes: ++\circ\circ\circ\,\circ
    • +
    • No: ++\circ\circ\circ\,\circ
    • +
    +

    Split 2:

    +
      +
    • Yes: ++\circ\circ\circ\circ\circ\circ\circ
    • +
    • No: ++\circ
    • +
    +

    Split 3:

    +
      +
    • Yes: \circ
    • +
    • No: ++++\circ\circ\circ\circ\circ\circ\circ
    • +
    +


    +

    Problem 10.1

    +

    Which of the six nodes above have the same entropy as the original +node? Select all that apply.

    +
      +
    • Split 1’s “Yes” node

    • +
    • Split 1’s “No” node

    • +
    • Split 2’s “Yes” node

    • +
    • Split 2’s “No” node

    • +
    • Split 3’s “Yes” node

    • +
    • Split 3’s “No” node

    • +
    +
    +
    +

    + +

    +
    +
    +
    +

    +
    +

    Answer: Split 1’s “Yes” node, Split 1’s “No” node, +and Split 2’s “No” node

    +

    The definition of entropy for a node is:

    +

    \text{entropy} = - \sum_C p_C \log_2 +p_C

    +

    where C is each label class, and +p_C is the proportion of points in the +node in class C.

    +

    We can note that in binary classification, two nodes will have the +same entropy if they have the same relative distribution of classes, or +if the distributions of classes are complements of each other. (For +example, a node with 75% positives and 25% negatives has the same +entropy as a node with 25% positives and 75% negatives.) So, in this +problem, we need only find nodes with the same proportions as the +original node, which has 4 positives (\frac{1}{3}) and 8 negatives (\frac{2}{3}).

    +
    +
    Difficulty: ⭐️⭐️
    +

    +

    The average score on this problem was 88%.

    +

    +
    +
    +
    +
    +


    +

    Problem 10.2

    +

    Which of the six nodes above have the lowest entropy? If there are +multiple correct answers, select them all.

    +
      +
    • Split 1’s “Yes” node

    • +
    • Split 1’s “No” node

    • +
    • Split 2’s “Yes” node

    • +
    • Split 2’s “No” node

    • +
    • Split 3’s “Yes” node

    • +
    • Split 3’s “No” node

    • +
    +
    +
    +

    + +

    +
    +
    +
    +

    +
    +

    Answer: Split 3’s “Yes” node

    +

    The lowest possible entropy for a distribution occurs when it takes +on only one value. In the definition of entropy, \log_2 p_C will be 0 when p_C is 1, so entropy will be zero when all +points are of the same class. This only occurs in one of the given +nodes, Split 3’s “Yes” node.

    +
    +
    Difficulty: ⭐️
    +

    +

    The average score on this problem was 93%.

    +

    +
    +
    +
    +
    +


    +
    +

    Problem 11

    +

    Jasmine and Aritra are trying to build models that predict the number +of open rooms a hotel room has. To do so, they use price, +the average listing price of rooms at the hotel, along with a one hot +encoded version of the hotel’s chain. For the +purposes of this question, assume the only possible hotel chains are +Marriott, Hilton, and Other.

    +


    +

    Problem 11.1

    +

    First, Jasmine fits a linear model without an intercept +term. Her prediction rule, H_1, looks +like:

    +

    H_{1}(x) = w_1 \cdot \texttt{price} + w_2 +\cdot \texttt{is\_Marriott} + w_3 \cdot \texttt{is\_Hilton} + w_4 \cdot +\texttt{is\_Other}

    +

    After fitting her model, \vec{w}^* = +\begin{bmatrix}−0.5 \\ 200 \\ 300 \\ 50 \end{bmatrix}.

    +
      +
    1. The Marriott Marquis San Diego Marina, a hotel in the Marriott +chain, has an average listing price of $250. How many open rooms does +H_1 predict it has? Give your answer as +a number with no variables.
    2. +
    3. The Marriott Marquis San Diego Marina actually has 45 open rooms. +What’s the squared loss of your prediction above? Give your answer as a +number with no variables.
    4. +
    5. True or False: Because your answer to (ii) above is not 0, it means +there were no hotels in the Marriott chain with an average listing price +of $250 in the training set. ( ) True ( ) False
    6. +
    +
    +
    +

    + +

    +
    +
    +
    +

    +
    +

    Answers:

    +
      +
    1. 75
    2. +
    3. 900
    4. +
    5. False
    6. +
    +

    If we plug in the weights from \vec{w}^* into the equation for H_1(x), noting that the values of the one-hot +variables are either 0 or 1, we get -0.5 \cdot +250 + 200 \cdot 1 + 300 \cdot 0 + 50 \cdot 0, or -125 + 200, or 75.

    +

    For part 2, the difference between predicted and actual number of +rooms is 75 - 45 = 30, and the squared +loss is simply 30^2 = 900.

    +

    For part 3, the answer is False, since the fact that our best-fit +line has an error at a given input does not mean that this input was not +seen in the training data. In other words, the line of best fit does not +always have to pass through all of the training points (and due to +overfitting, in most cases you don’t want it to).

    +
    +
    Difficulty: ⭐️⭐️
    +

    +

    The average score on this problem was 87%.

    +

    +
    +
    +
    +
    +


    +

    Problem 11.2

    +

    Then, on the same training set, Aritra fits a linear model, +with an intercept term but without the is_Other +feature. His new prediction rule, H_2, +now looks like:

    +

    H_2(x) = \beta_0 + \beta_1 \cdot +\texttt{price} + \beta_2 \cdot \texttt{is\_Marriott} + \beta_3 \cdot +\texttt{is\_Hilton}

    +

    After fitting his model, Aritra finds optimal coefficients \beta_{0}^{*}, \beta_{1}^{*}, \beta_{2}^{*}, and \beta_{3}^{*}.

    +
      +
    1. The training RMSE of H_2 is equal +to the training RMSE of H_1.
    2. +
    +
      +
    • True

    • +
    • False

    • +
    +
      +
    1. Assuming we use the same test set, the test RMSE of H_2 is equal to the test RMSE of H_1.
    2. +
    +
      +
    • True

    • +
    • False

    • +
    +
    +
    +

    + +

    +
    +
    +
    +

    +
    +

    Answers:

    +
      +
    1. True
    2. +
    3. True
    4. +
    +

    In model H_1, there is redundant +information in the one-hot encoded features, creating multicollinearity. +The second model H_2 removes the +is_Other feature, but the intercept term it is replaced +with serves a similar function. When is_Other is true, the +prediction of H_1 is w_1 \cdot \texttt{price} + w_4, and the +prediction of H_2 is \beta_1 \cdot \texttt{price} + \beta_0. The +multicollinearity in H_1 doesn’t affect +model performance relative to model 2, but it will yield different +parameter estimates since there will be multiple solutions, unlike with +H_2. However, the models will have +equivalent best solutions, even if the parameters differ, so both parts +are True.

    +
    +
    Difficulty: ⭐️⭐️⭐️
    +

    +

    The average score on this problem was 53%.

    +

    +
    +
    +
    +
    +


    +

    Problem 11.3

    +

    After fitting his model, Aritra finds \beta_{0}^{*} = 50. Given that, what are +\beta_{1}^{*}, \beta_{2}^{*}, and \beta_{3}^{*}? Give your answers as numbers +with no variables.

    +
    +
    +

    + +

    +
    +
    +
    +

    +
    +

    Answers:

    +
      +
    1. -0.5
    2. +
    3. 150
    4. +
    5. 250
    6. +
    +

    As we saw in the previous question, these models should yield an +equivalent best-fit line. The relationship between price +and predicted outcome will be the same, so \beta_{1}^{*} will be -0.5, the same weight as in H_1.

    +

    If \beta_{0}^{*} = 50, this means we +are adding 50 to all predictions, and that the “adjustments” we make to +the prediction for is_Marriott and is_Hilton +should therefore be reduced to compensate for this; therefore, the new +weights \beta_{2}^{*} and \beta_{3}^{*} will be 150 and 250.

    +
    +
    Difficulty: ⭐️⭐️⭐️
    +

    +

    The average score on this problem was 69%.

    +

    +
    +
    +
    +
    +


    +
    +

    Problem 12

    +

    Diego also wants to build a model that predicts the number of open +rooms a hotel has, given various other features. He has a training set +with 1200 rows available to him for the purposes of training his +model.

    +


    +

    Problem 12.1

    +

    Diego fits a regression model using the GPTRegression +class. GPTRegression models have several hyperparameters +that can be tuned, including context_length and +sentience.

    +

    To choose between 5 possible values of the hyperparameter +context_length, Diego performs k-fold cross-validation.

    +
      +
    1. How many total times is a GPTRegression model fit?
    2. +
    +
      +
    • 4k

    • +
    • 5k

    • +
    • 240k

    • +
    • 6000k

    • +
    • 4(k − 1)

    • +
    • 5(k − 1)

    • +
    • 240(k − 1)

    • +
    • 6000(k − 1)

    • +
    +
      +
    1. Suppose that every time a GPTRegression model is fit, +it appends the number of points in its training set to the list +sizes. Note that after performing cross- validation, +len(sizes) is equal to your answer to the previous +subpart.
    2. +
    +

    What is sum(sizes)?

    +
      +
    • 4k

    • +
    • 5k

    • +
    • 240k

    • +
    • 6000k

    • +
    • 4(k − 1)

    • +
    • 5(k − 1)

    • +
    • 240(k − 1)

    • +
    • 6000(k − 1)

    • +
    +
    +
    +

    + +

    +
    +
    +
    +

    +
    +

    Answers:

    +
      +
    1. 5k
    2. +
    3. 6000(k-1)
    4. +
    +

    When we do k-fold cross-validation +for one single hyperparameter value, we split the dataset into k folds, and in each iteration i, train the model on the remaining k-1 folds and evaluate on fold i. Since every fold is left out and evaluated +on once, the model is fit in total k +times. We do this once for every hyperparameter value we want to test, +so the total number of model fits required is 5k.

    +

    In part 2, we can note that each model fit is performed on the same +size of data – the size of the remaining k-1 folds when we hold out a single fold. +This size is 1 - \frac{1}{k} = +\frac{k-1}{k} times the size of the entire dataset, in this case, +1200 \cdot \frac{k-1}{k}, and we fit a +model on a dataset of this size 5k +times. So, the sum of the training sizes for each model fit is:

    +

    5k \cdot \frac{k-1}{k} \cdot 1200 = +6000(k-1)

    +
    +
    Difficulty: ⭐️⭐️⭐️
    +

    +

    The average score on this problem was 66%.

    +

    +
    +
    +
    +
    +


    +

    Problem 12.2

    +

    The average training error and validation error for all 5 candidate +values of context_length are given below.

    +
    +

    Fill in the blanks: As context_length increases, model +complexity __(i)__. The optimal choice of +context_length is __(ii)__; if we choose a +context_length any higher than that, our model will +__(iii)__.

    +
      +
    1. What goes in blank (i)?
    2. +
    +
      +
    • increases

    • +
    • decreases

    • +
    +
      +
    1. What goes in blank (ii)?
    2. +
    +
      +
    • 0.1

    • +
    • 1

    • +
    • 10

    • +
    • 100

    • +
    • 1000

    • +
    +
      +
    1. What goes in blank (iii)?
    2. +
    +
      +
    • overfit the training data and have high bias

    • +
    • underfit the training data and have high bias

    • +
    • overfit the training data and have low bias

    • +
    • underfit the training data and have low bias

    • +
    +
    +
    +

    + +

    +
    +
    +
    +

    +
    +

    Answers:

    +
      +
    1. decreases
    2. +
    3. 100
    4. +
    5. underfit the training data and have high bias
    6. +
    +

    In part 1, we can see that as context_length increases, +the training error increases, and the model performs worse. In general, +higher model complexity leads to better model performance, so here, +increasing context_length is reducing model +complexity.

    +

    In part 2, we will choose a context_length of 100, since +this parameterization leads to the best validation performance. If we +increase context_length further, the validation error +increases.

    +

    In part 3, since increased context_length indicates +less complexity and worse training performance, increasing the +context_length further would lead to underfitting, as the +model would lack the expressiveness or number of parameters required to +capture the data. Since training error represents model bias, and since +high variance is associated with overfitting, a further +increase in context_length would mean a more biased +model.

    +
    +
    Difficulty: ⭐️⭐️⭐️
    +

    +

    The average score on this problem was 65%.

    +

    +
    +
    +
    +
    +


    +
    +

    +

    👋 +Feedback: Find an error? Still confused? Have a suggestion? +Let us know +here.

    +
    + + diff --git a/docs/wi24-midterm/index.html b/docs/wi24-midterm/index.html index e495320..8bbd358 100644 --- a/docs/wi24-midterm/index.html +++ b/docs/wi24-midterm/index.html @@ -11,8 +11,11 @@ div.columns{display: flex; gap: min(4vw, 1.5em);} div.column{flex: auto; overflow-x: auto;} div.hanging-indent{margin-left: 1.5em; text-indent: -1.5em;} - ul.task-list{list-style: none;} + /* The extra [class] is a hack that increases specificity enough to + override a similar rule in reveal.js */ + ul.task-list[class]{list-style: none;} ul.task-list li input[type="checkbox"] { + font-size: inherit; width: 0.8em; margin: 0 0.8em 0.2em -1.6em; vertical-align: middle; @@ -189,7 +192,7 @@

    Click to view the solution.

    -
    @@ -235,7 +238,7 @@

    Click to view the solution.

    -
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    Click to view the solution.

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    Click to view the solution.

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    Click to view the solution.

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    Click to view the solution.

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    Click to view the solution.

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    Click to view the solution.

    -
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    Click to view the solution.

    -
    @@ -857,6 +860,11 @@

    the second dogs DataFrame. Since there are 12 in the first and 12 in the second, there are 12 \cdot 12 = 144 combinations.

    +
    +
    Difficulty: ⭐️⭐️⭐️⭐️
    +

    +

    The average score on this problem was 49%.

    +

    @@ -875,7 +883,7 @@

    Click to view the solution.

    -
    @@ -891,6 +899,11 @@

    corresponding to districts that appear 3 times. There are 40 districts that appear 3 times. So, the total number of rows in this DataFrame is 40 \cdot 3 = 120.

    +
    +
    Difficulty: ⭐️⭐️⭐️⭐️⭐️
    +

    +

    The average score on this problem was 16%.

    +

    @@ -915,7 +928,7 @@

    Click to view the solution.

    -
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    Click to view the solution.

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    Click to view the solution.

    -
    diff --git a/index.md b/index.md index e97cedb..e117dfe 100644 --- a/index.md +++ b/index.md @@ -10,8 +10,6 @@ title: Home – DSC 80 Practice This site contains practice problems taken from old DSC 80 exams. Each exam linked here lists the conditions under which the exam was given, including the allotted amount of time and the resources allowed. For the best preparation, work through all the questions on an exam in order under these same conditions, writing down your answers **on paper** as you go, then check all your answers at the end. It's especially important that you practice on paper, since your exams will also be on paper. Even though you will see some multiple choice bubbles, you intentionally cannot select them. - -
    -Midterm 🆕 +Midterm
    +Final 🆕
    Midterm
    -Final 🆕 +Final
    -Final 🆕 +Final
    Midterm
    -Final 🆕 +Final
    @@ -30,7 +28,9 @@ This site contains practice problems taken from old DSC 80 exams. Each exam link - @@ -38,14 +38,14 @@ This site contains practice problems taken from old DSC 80 exams. Each exam link @@ -53,7 +53,7 @@ This site contains practice problems taken from old DSC 80 exams. Each exam link diff --git a/pages/exams/sp23-midterm.yml b/pages/exams/sp23-midterm.yml deleted file mode 100644 index f719ee3..0000000 --- a/pages/exams/sp23-midterm.yml +++ /dev/null @@ -1,11 +0,0 @@ -title: 'Spring 2023 Midterm Exam' -instructors: Tauhidur Rahman -context: This exam was administered in-person. The exam was closed-notes, except students were allowed to bring a single two-sided cheat sheet. No calculators were allowed. Students had **50 minutes** to take this exam. -show_solution: true -problems: - - sp23-midterm/sp23-midterm-q01 - # - sp23-midterm/sp23-midterm-q02 - # - sp23-midterm/sp23-midterm-q03 - # - sp23-midterm/sp23-midterm-q04 - # - sp23-midterm/sp23-midterm-q05 - # - sp23-midterm/sp23-midterm-q06 \ No newline at end of file diff --git a/pages/exams/wi24-final.yml b/pages/exams/wi24-final.yml new file mode 100644 index 0000000..2593b14 --- /dev/null +++ b/pages/exams/wi24-final.yml @@ -0,0 +1,18 @@ +title: 'Winter 2024 Final Exam' +instructors: Suraj Rampure +context: This exam was administered in-person. The exam was closed-notes, except students were allowed to bring two two-sided notes sheets. No calculators were allowed. Students had **180 minutes** to take this exam. +show_solution: true +data_info: wi24-final/wi24-final-data-info +problems: + - wi24-final/wi24-final-q01 + - wi24-final/wi24-final-q02 + - wi24-final/wi24-final-q03 + - wi24-final/wi24-final-q04 + - wi24-final/wi24-final-q05 + - wi24-final/wi24-final-q06 + - wi24-final/wi24-final-q07 + - wi24-final/wi24-final-q08 + - wi24-final/wi24-final-q09 + - wi24-final/wi24-final-q10 + - wi24-final/wi24-final-q11 + - wi24-final/wi24-final-q12 \ No newline at end of file diff --git a/problems/wi24-final/wi24-final-data-info.md b/problems/wi24-final/wi24-final-data-info.md new file mode 100644 index 0000000..73950d6 --- /dev/null +++ b/problems/wi24-final/wi24-final-data-info.md @@ -0,0 +1,17 @@ +The DSC 80 staff are looking into hotels — some in San Diego, for their family to stay at for graduation, and some elsewhere, for summer trips. + +**In Question 1 only**, you will work with the DataFrame `hotels`. Each row of `hotels` contains information about a different hotel in San Diego. Specifically, for each hotel, we have: + +- `"Hotel Name" (str)`: The name of the hotel. **Assume hotel names are unique.** +- `"Location" (str):` The hotel's neighborhood in San Diego +- `"Chain" (str):` The chain the hotel is a part of; either `"Hilton", "Marriott", "Hyatt", or "Other".` A hotel chain is a group of hotels owned or operated by a shared company +- `"Number of Rooms" (int)`: The number of rooms the hotel has. + +The first few rows of `hotels` are shown below, but hotels has many more rows than are shown. + +
    + +Remember that `hotels` is only being used in Question 1; other questions will introduce other assumptions. + +**Throughout the exam**, assume we have already run the necessary import statements. + diff --git a/problems/wi24-final/wi24-final-q01.md b/problems/wi24-final/wi24-final-q01.md new file mode 100644 index 0000000..d07ea41 --- /dev/null +++ b/problems/wi24-final/wi24-final-q01.md @@ -0,0 +1,152 @@ +# BEGIN PROB + +Consider the variable `summed`, defined below. + +`summed = hotels.groupby("Chain")["Number of Rooms"].sum().idxmax()` + +# BEGIN SUBPROB + +What is `type(summed)`? + +( ) `int` +( ) `str` +( ) `Series` +( ) `DataFrame` +( ) `DataFrameGroupBy` + +# BEGIN SOLUTION + +**Answer:** `str` + +When we do a `groupby` on the `Chain` column in `hotels`, this means that the values in the `Chain` column will be the indices of the DataFrame or Series we get as output, in this case the Series `hotels.groupby("Chain")["Number of Rooms"].sum()`. + +Since the values of `Chain` are strings, and since `.idxmax()` will return a value from the index of the aforementioned Series, `summed` is a string. + +88 + +# END SOLUTION + +# END SUBPROB + +# BEGIN SUBPROB + +In one sentence, explain what the value of `summed` means. Phrase your explanation as if you had to give it to someone who is not a data science major; that is, don’t say something like “it is the result of grouping `hotels` by `"Chain"`, selecting the `"Number of Rooms"` column, ...”, but instead, give the value context. + +# BEGIN SOLUTION + +**Answer:** `summed` is the name of the hotel chain with the most total rooms + +The result of the `.groupby()` and `.sum()` is a Series indexed by the unique `Chains`, whose values are the total number of rooms in hotels owned by each chain. The `idxmax()` function gets the index corresponding to the largest value in the Series, which will be the hotel chain name with the most total rooms. + +97 + +# END SOLUTION + +# END SUBPROB + +# BEGIN SUBPROB + +Consider the variable `curious`, defined below. + +`curious = frame["Chain"].value_counts().idxmax()` + +Fill in the blank: `curious` is guaranteed to be equal to `summed` only if `frame` has one row for every ____ in San Diego. + +( ) hotel +( ) hotel chain +( ) hotel room +( ) neighborhood + +# BEGIN SOLUTION + +**Answer:** hotel room + +`curious` gets the most common value of `Chain` in the DataFrame `frame`. We already know that `summed` is the hotel chain with the most rooms in San Diego, so `curious` only equals `summed` if the most common `Chain` in `frame` is the hotel chain with the most total rooms; this occurs when each row of `frame` is a single hotel room. + +80 + +# END SOLUTION + +# END SUBPROB + +# BEGIN SUBPROB + +Fill in the blanks so that `popular_areas` is an array of the names of the unique neighborhoods that have at least 5 hotels and at least 1000 hotel rooms. + +```py + f = lambda df: __(i)__ + popular_areas = hotels.groupby(__(ii)__).__(iii)__.__(iv)__ +``` + +1. What goes in blank (i)? + +2. What goes in blank (ii)? + +( ) `"Hotel Name"` +( ) `"Location"` +( ) `"Chain"` +( ) `"Number of Rooms"` + +3. What goes in blank (iii)? + +( ) `agg(f)` +( ) `filter(f)` +( ) `transform(f)` + +4. What goes in blank (iv)? + +# BEGIN SOLUTION + +**Answers**: + +1. `df.shape[0] >= 5 and df["Number of Rooms"].sum() >= 1000` +2. `"Location"` +3. `filter(f)` +4. `["Location"].unique()` or equivalent + +We'd like to only consider certain neighborhoods according to group characteristics (having >= 5 hotels and >= 1000 hotel rooms), and `.filter()` allows us to do that by excluding groups not meeting those criteria. So, we can write a function that evaluates those criteria on one group at a time (the `df` of input to `f` is the subset of `hotels` containing just one `Location` value), and calling `filter(f)` means that the only remaining rows are hotels in neighborhoods that match those criteria. Finally, all we have to do is get the unique neighborhoods from this DataFrame, which are the neighborhoods for which `f` returned `True`. + +83 + +# END SOLUTION + +# END SUBPROB + +# BEGIN SUBPROB + +Consider the code below. + +```py + cond1 = hotels["Chain"] == "Marriott" + cond2 = hotels["Location"] == "Coronado" + combined = hotels[cond1].merge(hotels[cond2], on="Hotel Name", how=???) +``` + +1. If we replace `???` with `"inner"` in the code above, which of the following will be equal to `combined.shape[0]`? + +2. If we replace `???` with `"outer"` in the code above, which of the following will be equal to `combined.shape[0]`? + +# BEGIN SOLUTION + +**Answers**: + +1. `(cond1 & cond2).sum()` +2. `cond1.sum() + cond2.sum() - (cond1 & cond2).sum()` + +Note that `cond1` and `cond2` are boolean Series, and `hotels[cond1]` and `hotels[cond2]` are the subsets of `hotels` where `Chain == "Marriott` and `"Location" == "Coronado"`, respectively. + +1. When we perform an inner merge, we're selecting every row where a `Hotel Name` appears in *both* `hotels[cond1]` and `hotels[cond2]`. This is the same set of indices (and therefore hotel names, since those are unique) as where `(cond1 & cond2) == True`. So, the length of `combined` will be the same as the number of `True`s in `(cond1 & cond2)`. + +2. When we perform an outer merge, we're selecting every row that appears in *either* DataFrame, although there will not be repeats for hotels that are both Marriott properties and are in Coronado. So, to find the total number of rows in either DataFrame, we take the sum of the sizes of each, and subtract rows that appear in both, which corresponds to answer `cond1.sum() + cond2.sum() - (cond1 & cond2).sum()`. + +79 + +# END SOLUTION + +# END SUBPROB + +# END PROB + + + + diff --git a/problems/wi24-final/wi24-final-q02.md b/problems/wi24-final/wi24-final-q02.md new file mode 100644 index 0000000..62b00ac --- /dev/null +++ b/problems/wi24-final/wi24-final-q02.md @@ -0,0 +1,179 @@ +# BEGIN PROB + +At the Estancia La Jolla, the hotel manager enters information about each reservation in the DataFrame `guests`, after guests check into their rooms. Specifically, `guests` has the columns: + +- `"id" (str):` The booking ID (e.g. `"SN1459"`). +- `"age" (int):` The age of the primary occupant (the person who made the reservation). +- `"people" (int):` The total number of occupants. +- `"is_business" (str):` Whether or not the trip is a business trip for the primary occupant (possible values: `"yes"`, `"no"`, and `"partially"`). +- `"company" (str):` The company that the primary occupant works for, if this is a business trip. +- `"loyalty" (int):` The loyalty number of the primary occupant. Note that most business travelers have a loyalty number. + +Some of the values in `guests` are missing. + +# BEGIN SUBPROB + +What is the most likely missingness mechanism of the `"loyalty"` column? + +( ) Missing by design +( ) Missing at random +( ) Not missing at random +( ) Missing completely at random + +# BEGIN SOLUTION + +**Answer:** missing at random + +The description of `loyalty` indicates that most business travelers have a loyalty number -- in other words, that depending on the value of `is_business`, the probability of a present value for `loyalty` can increase or decrease. This is therefore an example of MAR. + +67 + +# END SOLUTION + +# END SUBPROB + +# BEGIN SUBPROB + +What is the most likely missingness mechanism of the `"company"` column? + +( ) Missing by design +( ) Missing at random +( ) Not missing at random +( ) Missing completely at random + +# BEGIN SOLUTION + +**Answer:** missing by design + +The value of `company` is missing if the trip is a business trip, and since this relationship should be deterministic, then this column is missing by design. + +60 + +# END SOLUTION + +# END SUBPROB + +# BEGIN SUBPROB + +Fill in the blanks: To assess whether the missingness of `"is_business"` depends on `"age"`, we should perform a `__(i)__` with `__(ii)__` as the test statistic. + +1. What goes in blank (i)? + +( ) standard hypothesis test +( ) permutation test + +2. What goes in blank (ii)? + +( ) the total variation distance +( ) the sample mean +( ) the (absolute) difference in means +( ) the K-S statistic +( ) either the (absolute) difference in means or the K-S statistic, depending on the shapes of the observed distributions + +# BEGIN SOLUTION + +**Answers:** + +1. permutation test +2. either the (absolute) difference in means or the K-S statistic, depending on the shapes of the observed distributions + +In part 1, we use a permutation test because we're comparing two sampled distributions (the values of `age` for rows with missing vs. present values of `is_business`), rather than comparing our sample distribution to a known population distribution/metric. + +For part 2, we should note that the test statistic, for each iteration of our permutation test, is meant to compare two distributions of the variable `age`, which is continuous. TVD is not well-suited for this, since it compares discrete, categorical distributions, and neither is "sample mean," since we have two samples to compare. Differences in means or the K-S statistic work because they both compare two continuous distributions. However, there are cases in which the difference in means might not capture differences in distributions (for example, two distributions with the same mean but very different standard deviation); this is the reason for the caveat in the correct solution. + +68 + +# END SOLUTION + +# END SUBPROB + +# BEGIN SUBPROB + +Fill in the blanks: To assess whether the missingness of `"age"` depends on `"is business"`, we should perform a `__(i)__` with `__(ii)__` as the test statistic. + +1. What goes in blank (i)? + +( ) standard hypothesis test +( ) permutation test + +2. What goes in blank (ii)? + +( ) the total variation distance +( ) the sample mean +( ) the (absolute) difference in means +( ) the K-S statistic +( ) either the (absolute) difference in means or the K-S statistic, depending on the shapes of the observed distributions + +# BEGIN SOLUTION + +**Answers:** + +1. permutation test +2. total variation distance + +For part 1, the reasoning is the same as the previous part -- the only difference is that now, we're comparing two categorical distributions rather than two continuous ones. + +In part 2, we can note that we're now comparing the categorical distributions of `is_business`, which can only have values of `"yes"`, `"no"`, and `"partially"`, for rows with missing vs. present values of `age`. (Even though `age` is continuous, since we're only using whether or not `age` is missing and not the actual values in the column, this doesn't really matter.) The only test statistic listed that is meant to compare two categorical distributions is TVD, so this is the correct solution. + +72 + +# END SOLUTION + +# END SUBPROB + +# BEGIN SUBPROB + +After running the code below, `p` is equal to the simulated p-value for a statistical test. + +```py + obs = guests.groupby("is_business")["age"].median().loc["no"] + p = 0 + for _ in range(10000): + s = guests.sample((guests["is_business"] == "no").sum(), + replace=False) + sm = s["age"].median() + p += (obs >= sm) / 10000 +``` + +1. What type of test is this? + +( ) standard hypothesis test +( ) permutation test + +Fill in the blanks: The alternative hypothesis being tested above is that the median age of primary occupants **not** on a business trip is `__(ii)__` the median age of `__(iii)__`. + +2. What goes in blank (ii)? + +( ) greater than or equal to +( ) greater than +( ) equal to +( ) not equal to +( ) less than or equal to +( ) less than + +3. What goes in blank (iii)? + +( ) all primary occupants +( ) primary occupants at least partially on a business trip (that is, primary occupants who have an `"is_business"` value of `"yes"` or `"partially"`) + +# BEGIN SOLUTION + +**Answers:** + +1. standard hypothesis test +2. less than +3. all primary occupants + +For part 1, this is a standard hypothesis test, because instead of shuffling the values of a particular column, we are sampling entire rows of the DataFrame; the size of these samples is the same as the number of guests who are not (even partially) on business trips. By sampling randomly from the entire DataFrame, this assumes the null hypothesis that the distribution of age of primary occupants *not* on a business trip is equal to the distribution of age for occupants as a whole. Therefore, this procedure is meant to simulate values of the median `age` of a sample of size `guests["is_business"] == "no").sum()`, and sampling random rows means that we're assuming that `is_business == "no"` and `age` are unrelated. + +For part 2, the samples capture how likely the deviation of the observed statistic is to happen under the null hypothesis, but the p-value is being calculated by adding up whenever the observed statistic is greater or equal to the sample. This indicates that we're doing a one-tailed test, and since to reject the null hypothesis and provide some evidence towards the alternate hypothesis, the p-value should be lower, the alternate hypothesis should be the complement of `obs >= sum`. + +For part 3, the answer is "all primary occupants" because our sampling procedure doesn't sample just from (full or partial) business travelers, but from the entire DataFrame. (In the line where we sample, the only arguments are the number of rows we're sampling, and that we're doing so without replacement -- nothing about restricting which rows in `guest` to sample.) In other words, we're not comparing primary occupants not on business trips to those on business trips, but rather we're comparing primary occupants to the entire dataset of occupants. + +58 + +# END SOLUTION + +# END SUBPROB + +# END PROB diff --git a/problems/wi24-final/wi24-final-q03.md b/problems/wi24-final/wi24-final-q03.md new file mode 100644 index 0000000..c15d274 --- /dev/null +++ b/problems/wi24-final/wi24-final-q03.md @@ -0,0 +1,88 @@ +# BEGIN PROB + +Weiyue proposes the following imputation scheme. + +```py + def impute(s): + return s.fillna(np.random.choice(s[s.notna()])) +``` + +# BEGIN SUBPROB + +**True or False:** `impute` performs probabilistic imputation, using the same definition of probabilistic imputation we learned about in class. + +( ) True +( ) False + +# BEGIN SOLUTION + +**Answer:** False + +In `impute`, `np.random.choice` will return a single non-null value from `s`, and `.fillna()` will fill every null value with this single value. Meanwhile, probabilistic imputation draws a different value from a specified distribution to fill each missing value, making it such that there won't be a single "spike" in the imputed distribution at a single chosen value. + +41 + +# END SOLUTION + +# END SUBPROB + +# BEGIN SUBPROB + +Consider the following expressions and values. + +``` + >>> vals.isna().mean() + 0.2 + >>> vals.describe().loc[["min", "mean", "max"]] + min 2.0 + mean 4.0 + max 7.0 + dtype: float64 +``` + +Given the above, what is the **maximum** possible value of `impute(vals).mean()`? +Give your answer as a number rounded to one decimal place. + +# BEGIN SOLUTION + +**Answer:** 4.6 + +The maximum possible value of `impute(vals).mean()` would occur when every single missing value in `vals` is filled in with the highest possible non-null value in `vals`. (As discussed in the previous solution, `impute` selects only one value from `s` to fill into every missing space.) + +If this occurs, then the mean of the imputed Series will be weighted mean of the available data and the filled data, and given the numbers in the question, this is $0.8 \cdot 4 + 0.2 \cdot 7$, or 4.6. + +50 + +# END SOLUTION + +# END SUBPROB + +# BEGIN SUBPROB + +Which of the following statements below will always evaluate to `True`? + +( ) `vals.std() < impute(vals).std()` +( ) `vals.std() <= impute(vals).std()` +( ) `vals.std() == impute(vals).std()` +( ) `vals.std() >= impute(vals).std()` +( ) `vals.std() > impute(vals).std()` +( ) None of the above + +# BEGIN SOLUTION + +**Answer:** None of the above + +Since the value which `impute()` will choose to impute with is random, the effect that it has on the standard deviation of `vals` is unknown. If the missing values are filled with a value close to the mean, this could reduce standard deviation; if they are filled with a value far from the mean, this could increase standard deviation. (Of course, the imputation will also shift the mean, so without knowing details of the Series, it's impossible to come up with thresholds.) In any case, since the value for imputation is chosen at random, none of these statements will *always* be true, and so the correct answer is "none of the above." + +38 + +# END SOLUTION + +# END SUBPROB + +# END PROB + + + + + diff --git a/problems/wi24-final/wi24-final-q04.md b/problems/wi24-final/wi24-final-q04.md new file mode 100644 index 0000000..343fdd2 --- /dev/null +++ b/problems/wi24-final/wi24-final-q04.md @@ -0,0 +1,88 @@ +# BEGIN PROB + +Suppose `site` is a `BeautifulSoup` object instantiated on the HTML document below. + +```html + +
    +

    Luxury Hotels in Bali from May 2-6, 2024 for Ethan

    +
    +

    Hilton Properties in Bali

    +
    +
    +

    Marriott Properties in Bali

    +
    +
    + __(ii)__ +
    +
    + +``` + +# BEGIN SUBPROB + +What does `len(site.find_all("div"))` evaluate to? Give your answer as an integer. For this part only, assume that both blank (i) and blank (ii) are left blank. + +# BEGIN SOLUTION + +**Answer:** 4 + +The answer simply requires counting the number of `div` elements, making sure not to double-count opening and closing tags. + +82 + +# END SOLUTION + +# END SUBPROB + +# BEGIN SUBPROB + +Fill in the blank so that `chain_color` takes in the name of a hotel chain and returns the color used to display the hotel chain in site. For example, `chain_color("Hilton")` should return `"blue"` and `chain_color("Marriott")` should return `"red"`. + +```py +chain_color = lambda chain: site.____.split()[-1] +``` + +# BEGIN SOLUTION + +**Answer:** `find("div", attrs={"name": chain}).find("h3").get("style")` + +The solution finds all `div` elements whose `name` attribute is equal to the function input `chain` (which is how the chains are defined in the HTML document). Then, the colors are stored as part of the `style` attribute in an `h3` tag within that `div`, so we find the first -- and in this document, only -- `h3` tag within the `div` and get its `style` attribute. This returns a string like `color: red`, from which the given code `.split()[-1]` returns the last word, which is the correct color. + +67 + +# END SOLUTION + +# END SUBPROB + +# BEGIN SUBPROB + +Fill in blanks (i) and (ii) in `site` so that the following all evaluate to True: + +- `len(site.find all("div", class ="chain")) == 2` +- `chain_color("Hyatt") == "purple"` +- `site.find all("div")[-1].text == ""` + +1. What goes in blank (i)? +2. What goes in blank (ii)? + +# BEGIN SOLUTION + +**Answers:** + +1. `name = "Hyatt"` +2. `

    ` + +In order to make all of the three given statements true, we need to make it such that there are 2 `div` elements with class `chain`, the `chain_color` function returns `purple` for `Hyatt`, and the last `div` tag in the document has no text. + +We do this by defining a `div` similar to the previous two, but without the `chain` class (because there are already 2 in the document). In order for `chain_color("Hyatt")` to return `purple`, we add `"Hyatt"` as a `name` attribute in the `div`, and add an `h3` tag within that `div` with `style="color: purple"`. However, since the last statement requires the last `div` in the document has no text, and the `div` we're currently making will be the final one, we don't include any text in the `h3` tag. (Note that because the `chain_color` function doesn't use the hotel name in the text to find a given chain's name, but rather the name attribute in the enclosing `div` tag.) + +90 + +# END SOLUTION + +# END SUBPROB + +# END PROB + + diff --git a/problems/wi24-final/wi24-final-q05.md b/problems/wi24-final/wi24-final-q05.md new file mode 100644 index 0000000..df55ffb --- /dev/null +++ b/problems/wi24-final/wi24-final-q05.md @@ -0,0 +1,85 @@ +# BEGIN PROB + +Dylan finds a messy text file containing room availability and pricing information at his favorite local hotel, the Manchester Grand Hyatt. + +# BEGIN SUBPROB + +Availability strings are formatted like so: + +``` + avail = """Standard: Available, This23: Available, + Suite: Available, Economy: Not Available, + Rooms are Available, Deluxe: Available""" +``` + +Fill in the blank below so that `exp1` is a regular expression such that if `s` is an availability string in the format above, `re.findall(exp1, s)` will return a list of all of the available room categories in `s`. Example behavior is given below. + +```py + >>> re.findall(exp1, avail) + ["Standard", "Suite", "Deluxe"] # Categories don't include numbers +``` + +Note that your answer needs to work on other availability strings; you should not hard-code `"Standard"`, `"Suite"`, or `"Deluxe"`. + +``` +exp1 = r"_____________" +``` + +# BEGIN SOLUTION + +**Answer:** `([A-Za-z]+): Available` + +In the above availability strings, we're looking for a one-or-more-length sequence of letters (not numbers, as mentioned in the problem), followed by a colon and the word "Available." However, since we only want to return the room type, and not the colon or the word "Available," we use a capturing group (the parentheses) to just return the word before the colon. + +57 + +# END SOLUTION + +# END SUBPROB + +# BEGIN SUBPROB + +Consider the string `prices`, defined below. + +```py + one = "Standard room: $120, $2.Deluxe room: $200.75" + two = "Other: 402.99, Suite: $350.25" + prices = one + ", " + two +``` + +1. What does `re.findall(r"\$\d+\.\d{2}$", prices)` evaluate to? + +( ) `["$200.75", "$402.99", "$350.25"]` +( ) `["200.75", "402.99", "350.25"]` +( ) `["$120", "$200.75", "$350.25"]` +( ) `["$350.25"]` +( ) `["$200.75", "$350.25"]` + +2. What does `re.findall(r"\$?(\d+\.\d{2})", prices)` evaluate to? + +( ) `["$200.75", "$402.99", "$350.25"]` +( ) `["200.75", "402.99", "350.25"]` +( ) `["$120", "$200.75", "$350.25"]` +( ) `["$350.25"]` +( ) `["$200.75", "$350.25"]` + +# BEGIN SOLUTION + +**Answers:** + +1. `["$350.25"]` +2. `["200.75", "402.99", "350.25"]` + +In the first part, the string that the pattern matches is a dollar sign (`$`), one or more digits (`\d+`), a period (`\.`), two digits (`\d{2}`), followed by the end of the string (`$`). Since the string we're passing into `re.findall` is `prices`, which is the concatenation of `one + ", " + two`, the only option that matches is the last price displayed, `"$350.25"`. (If we had not specified the match ending with the end of the string, `"$200.75"` would also have been a match.) + +In the second part, the beginning of the pattern is `"\$?"`, which means to match *zero or one* instance of the dollar sign character. In most cases, this means that if there is a dollar sign before the remainder of the pattern, it will be included in the match, but if not, the rest of the pattern will still match. However, the capturing group around the remainder of the pattern means that in either case, only the remainder of the pattern after the dollar sign is captured. (So, in this particular example, the `\$?` has no effect on the output.) + +The rest of the pattern is structured similarly to the previous part, except now, the pattern does not require the end of the string after the price, so we're just selecting sequences of digits followed by a period and two more digits, which is how we get our solution. + +65 + +# END SOLUTION + +# END SUBPROB + +# END PROB \ No newline at end of file diff --git a/problems/wi24-final/wi24-final-q06.md b/problems/wi24-final/wi24-final-q06.md new file mode 100644 index 0000000..cbf1e85 --- /dev/null +++ b/problems/wi24-final/wi24-final-q06.md @@ -0,0 +1,47 @@ +# BEGIN PROB + +Gabriel decides to look at reviews for the Catamaran Resort Hotel and Spa. TripAdvisor has 96 reviews for the hotel; of those 96, Gabriel’s favorite review was: + +``` + "close to the beach but far from the beach beach" +``` + +# BEGIN SUBPROB + +What is the TF of `"beach"` in Gabriel’s favorite review? Give your answer as a simplified fraction. + +# BEGIN SOLUTION + +**Answer:** $\frac{3}{10}$ + +The answer is simply the proportion of words in the sentence that are the word `"beach"`. There are 10 words in the sentence, 3 of which are `"beach"`. + +97 + +# END SOLUTION + +# END SUBPROB + +# BEGIN SUBPROB + +The TF-IDF of `"beach"` in Gabriel’s favorite review is $\frac{9}{10}$, when using a base-2 logarithm to compute the IDF. How many of the reviews on TripAdvisor for this hotel contain the term `"beach"`? + +# BEGIN SOLUTION + +**Answer:** 12 + +The TF-IDF is the product of the TF and IDF terms. So if the TF-IDF of this document is $\frac{9}{10}$, and the TF is $\frac{3}{10}$, as established in the last part, the IDF of the term `"beach"` is 3. The IDF for a word is the log of the inverse of the proportion of documents in which the word appears. So, since we know there are 96 total documents. + +$$3 = log_{2}(\frac{96}{\text{\# documents containing "beach"}})$$ + +$$2^{3} = \frac{96}{\text{\# documents containing "beach"}}$$ + +$$\boxed{12} = {\text{\# documents containing "beach"}}$$ + +76 + +# END SOLUTION + +# END SUBPROB + +# END PROB \ No newline at end of file diff --git a/problems/wi24-final/wi24-final-q07.md b/problems/wi24-final/wi24-final-q07.md new file mode 100644 index 0000000..8e12d32 --- /dev/null +++ b/problems/wi24-final/wi24-final-q07.md @@ -0,0 +1,37 @@ +# BEGIN PROB + +Tiffany decides to look at reviews for the same hotel, but she modifies them so that the only terms they contain are `"taco"` and `"sand"`. The bag-of-words representations of three reviews are shown as vectors below. + +
    + +Using cosine similarity to measure similarity, which pair of reviews are the most similar? If there are multiple pairs of reviews that are most similar, select them all. + +[ ] $\vec{r}_1$ and $\vec{r}_2$ +[ ] $\vec{r}_1$ and $\vec{r}_3$ +[ ] $\vec{r}_2$ and $\vec{r}_3$ + +# BEGIN SOLUTION + +**Answer:** $\vec{r}_1$ and $\vec{r}_2$, **and** $\vec{r}_2$ and $\vec{r}_3$ + +The cosine similarity of two vectors $\vec{a}$ and $\vec{b}$ is $\frac{\vec{a} \cdot \vec{b}}{||\vec{a}|| \cdot ||\vec{b}||}$. + +The cosine similarity of $\vec{r}_1$ and $\vec{r}_2$ is: + +$$\frac{2 \cdot 4 + 3 \cdot 4}{\sqrt{13} \cdot \sqrt{32}} = \frac{20}{4 \cdot \sqrt{26}} = \frac{5}{\sqrt{26}}$$ + +The cosine similarity of $\vec{r}_1$ and $\vec{r}_3$ is: + +$$\frac{2 \cdot 6 + 3 \cdot 4}{\sqrt{13} \cdot \sqrt{52}} = \frac{24}{26} = \frac{12}{13}$$ + +The cosine similarity of $\vec{r}_2$ and $\vec{r}_3$ is: + +$$\frac{4 \cdot 6 + 4 \cdot 4}{\sqrt{32} \cdot \sqrt{52}} = \frac{40}{8 \cdot \sqrt{26}} = \frac{5}{\sqrt{26}}$$ + +$\frac{12}{13} \approx 0.9231$, and $\frac{5}{\sqrt{26}} \approx 0.9806$, so our answer is vector pairs $\vec{r}_1$ and $\vec{r}_2$, and $\vec{r}_2$ and $\vec{r}_3$ + +74 + +# END SOLUTION + +# END PROB \ No newline at end of file diff --git a/problems/wi24-final/wi24-final-q08.md b/problems/wi24-final/wi24-final-q08.md new file mode 100644 index 0000000..ad13399 --- /dev/null +++ b/problems/wi24-final/wi24-final-q08.md @@ -0,0 +1,87 @@ +# BEGIN PROB + +Consider the corpus of length 13 below, made up of 6 As, 4 Bs, 1 C, and 2 Rs (and no other tokens). Here, each individual character is treated as its own token. + +$$\text{ABABRACABABRA}$$ + +Let $P$ be a function that computes the probability of the input sequence using a bigram model trained on the above corpus. For example, $P$(BR) is the probability of the sequence BR, using a bigram language model trained on the above corpus. + +# BEGIN SUBPROB + +What is $P$(ABRA)? Give your answer as a simplified fraction. + +# BEGIN SOLUTION + +**Answer:** $\frac{12}{65}$ + +Using a bigram model, we find the probability of the first token, then for each remaining token, find its probability given just the previous token. The probability $P(\text{X} | \text{Y})$ is simply the proportion of times that token X is the next token after the previous token Y. So, for this corpus and input sequence, we have: + +$$P(\text{A}) = \frac{6}{13}$$ + +$$P(\text{B} | \text{A}) = \frac{4}{5}$$ + +$$P(\text{R} | \text{B}) = \frac{2}{4} = \frac{1}{2}$$ + +$$P(\text{A} | \text{R}) = \frac{2}{2} = 1$$ + +So, we just have to multiply these probabilities together, and we get $\frac{12}{65}$. + +Note that the denominator for $P(\text{B} | \text{A})$ is 5, not 6, even though there are 6 occurrences of the letter A. This is because the final one occurs at the end of the sentence, and we're not using a stop token or anything else designating the end of the sequence. So there are only 5 instances of "A" where we have a subsequent token, which is how we make our probability model. + +47 + +# END SOLUTION + +# END SUBPROB + +# BEGIN SUBPROB + +Suppose $n$ is a positive integer. Let $[AB]^{n}$ be the result of repeating the sequence AB $n$ times. For example, $[AB]^{4}$ is ABABABAB and $[AB]^{5}$ is ABABABABAB. + +Then, it is always the case that: + +$$P([AB]^{n}) = 2p (\frac{c}{d})^{k}$$ + +where: + +- $p = P$(ABRA) is your answer to part (a) +- $c$ and $d$ are positive integers that don't depend on $n$, and $\frac{c}{d}$ is a simplified fraction +- $k$ is a positive number that does depend on $n$ + +1. What is $c$? Give your answer as a positive integer. Remember, your answer should *not* depend on $n$, meaning that it should have no variables in it. +2. What is $d$? Give your answer as a positive integer. Remember, your answer should *not* depend on $n$, meaning that it should have no variables in it. +3. What is $k$? + +( ) 2 +( ) $\frac{n}{2} - 1$ +( ) $\frac{n}{2}$ +( ) $n - 1$ +( ) $n$ +( ) $n + 1$ + +*Hint: Start by finding P(AB), P(ABAB), and P(ABABAB).* + +# BEGIN SOLUTION + +**Answer:** + +1. $c = 2$ +2. $d = 5$ +3. $k = n-1$ + +From our work on the previous question, we can see that $2p$ is equal to $P(\text{A}) \cdot P(\text{B} | \text{A})$, or in other words, the probability of the sequence AB. + +The probability of sequence ABAB will be the probability of sequence AB, times $P(\text{A} | \text{B}) \cdot P(\text{B} | \text{A})$. More generally, we can see that after the first pair of tokens AB (which has a different probability since the first token is the first in the sequence, and therefore isn't conditioned on B), each repetition of AB multiplies a probability of $P(\text{A} | \text{B}) \cdot P(\text{B} | \text{A})$. + +Therefore, our resulting fraction $\frac{c}{d}$ is simply this probability $P(\text{A} | \text{B}) \cdot P(\text{B} | \text{A})$. $P(\text{A} | \text{B})$ is $\frac{1}{2}$, and we already found that $P(\text{B} | \text{A})$ is $\frac{4}{5}$, so the resulting fraction is $\frac{2}{5}$. So $c$ = 2, and $d$ = 5. + +This fraction is multiplied once for each repetition of AB *after the first one* (which has a different probability, represented by $2p$), and so the exponent should be $n-1$. + +66 + +# END SOLUTION + +# END SUBPROB + +# END PROB + diff --git a/problems/wi24-final/wi24-final-q09.md b/problems/wi24-final/wi24-final-q09.md new file mode 100644 index 0000000..eade3b0 --- /dev/null +++ b/problems/wi24-final/wi24-final-q09.md @@ -0,0 +1,120 @@ +# BEGIN PROB + +Suppose Yutian builds a classifier that predicts whether or not a hotel provides free parking. The confusion matrix for her classifier, when evaluated on our training set, is given below. + +
    + +# BEGIN SUBPROB + +What is the precision of Yutian’s classifier? Give your answer as a simplified fraction. + +# BEGIN SOLUTION + +**Answer:** $\frac{8}{13}$ + +Precision is the proportion of predicted positives that actually were positives. So, given this confusion matrix, that value is $\frac{8}{8 + 5}$, or $\frac{8}{13}$. + +89 + +# END SOLUTION + +# END SUBPROB + +# BEGIN SUBPROB + +Fill in the blanks: In order for Yutian’s classifier’s recall to be equal to its precision, `__(i)__` must be equal to `__(ii)__`. + +1. What goes in blank (i)? + +( ) $A$ +( ) $B$ + +2. What goes in blank (ii)? + +( ) 2 +( ) 3 +( ) 4 +( ) 5 +( ) 6 +( ) 8 +( ) 13 +( ) 14 +( ) 20 +( ) 40 +( ) 50 +( ) 80 + +# BEGIN SOLUTION + +**Answer:** + +1. $B$ +2. 5 + +We already know that the precision is $\frac{8}{13}$. Recall is the proportion of true positives that were indeed classified positives, which in this matrix is $\frac{8}{B + 8}$. So, in order for precision to equal recall, $B$ must be 5. + +96 + +# END SOLUTION + +# END SUBPROB + +# BEGIN SUBPROB + +Now, suppose both $A$ and $B$ are unknown. Fill in the blanks: In order for Yutian’s classifier’s recall to be equal to its accuracy, `__(i)__` must be equal to `__(ii)__`. + +1. What goes in blank (i)? + +( ) $A + B$ +( ) $A - B$ +( ) $B - A$ +( ) $A \cdot B$ +( ) $\frac{A}{B}$ +( ) $\frac{B}{A}$ + +2. What goes in blank (ii)? + +( ) 2 +( ) 3 +( ) 4 +( ) 5 +( ) 6 +( ) 8 +( ) 13 +( ) 14 +( ) 20 +( ) 40 +( ) 50 +( ) 80 + +*Hint: To verify your answer, pick an arbitrary value of A, like A = 10, and solve for the B that sets the model’s recall equal to its accuracy. Do the specific A and B you find satisfy your answer above?* + +# BEGIN SOLUTION + +**Answer:** + +1. $A \cdot B$ +2. 40 + +We can solve this problem by simply stating recall and accuracy in terms of the values in the confusion matrix. As we already found, recall is $\frac{8}{B+8}$. Accuracy is the sum of correct predictions over total number of predictions, or $\frac{A + 8}{A + B + 13}$. Then, we simply set these equal to each other, and solve. + +$$\frac{8}{B+8} = \frac{A + 8}{A + B + 13}$$ +$$8(A + B + 13) = (A + 8)(B + 8)$$ +$$8A + 8B + 104 = AB + 8A + 8B + 64$$ +$$104 = AB + 64$$ +$$AB = 40$$ + +79 + +# END SOLUTION + +# END SUBPROB + +# END PROB + + + + + + + diff --git a/problems/wi24-final/wi24-final-q10.md b/problems/wi24-final/wi24-final-q10.md new file mode 100644 index 0000000..2492a3e --- /dev/null +++ b/problems/wi24-final/wi24-final-q10.md @@ -0,0 +1,78 @@ +# BEGIN PROB + +Harshi is trying to build a decision tree that predicts whether or not a hotel has a swimming pool. + +Suppose $+$ represents the “has pool” class and $\circ$ represents the “no pool” class. One of the nodes in Harshi’s decision tree has 12 points, with the following distribution of classes. + +$$++++\circ\circ\circ\circ\circ\circ\circ\,\circ$$ + +Consider the following three splits of the node above. + +Split 1: + +- Yes: $++\circ\circ\circ\,\circ$ +- No: $++\circ\circ\circ\,\circ$ + +Split 2: + +- Yes: $++\circ\circ\circ\circ\circ\circ\circ$ +- No: $++\circ$ + +Split 3: + +- Yes: $\circ$ +- No: $++++\circ\circ\circ\circ\circ\circ\circ$ + +# BEGIN SUBPROB + +Which of the six nodes above have the same entropy as the original node? Select all that apply. + +[ ] Split 1’s “Yes” node +[ ] Split 1’s “No” node +[ ] Split 2’s “Yes” node +[ ] Split 2’s “No” node +[ ] Split 3’s “Yes” node +[ ] Split 3’s “No” node + +# BEGIN SOLUTION + +**Answer:** Split 1’s “Yes” node, Split 1’s “No” node, and Split 2’s “No” node + +The definition of entropy for a node is: + +$$\text{entropy} = - \sum_C p_C \log_2 p_C$$ + +where $C$ is each label class, and $p_C$ is the proportion of points in the node in class $C$. + +We can note that in binary classification, two nodes will have the same entropy if they have the same relative distribution of classes, or if the distributions of classes are complements of each other. (For example, a node with 75% positives and 25% negatives has the same entropy as a node with 25% positives and 75% negatives.) So, in this problem, we need only find nodes with the same proportions as the original node, which has 4 positives ($\frac{1}{3}$) and 8 negatives ($\frac{2}{3}$). + +88 + +# END SOLUTION + +# END SUBPROB + +# BEGIN SUBPROB + +Which of the six nodes above have the lowest entropy? If there are multiple correct answers, select them all. + +[ ] Split 1’s “Yes” node +[ ] Split 1’s “No” node +[ ] Split 2’s “Yes” node +[ ] Split 2’s “No” node +[ ] Split 3’s “Yes” node +[ ] Split 3’s “No” node + +# BEGIN SOLUTION + +**Answer:** Split 3’s “Yes” node + +The lowest possible entropy for a distribution occurs when it takes on only one value. In the definition of entropy, $\log_2 p_C$ will be 0 when $p_C$ is 1, so entropy will be zero when all points are of the same class. This only occurs in one of the given nodes, Split 3’s “Yes” node. + +93 + +# END SOLUTION + +# END SUBPROB + +# END PROB \ No newline at end of file diff --git a/problems/wi24-final/wi24-final-q11.md b/problems/wi24-final/wi24-final-q11.md new file mode 100644 index 0000000..8fd292d --- /dev/null +++ b/problems/wi24-final/wi24-final-q11.md @@ -0,0 +1,94 @@ +# BEGIN PROB + +Jasmine and Aritra are trying to build models that predict the number of open rooms a hotel room has. To do so, they use `price`, the average listing price of rooms at the hotel, along with a one hot encoded version of the hotel’s `chain`. **For the purposes of this question, assume the only possible hotel chains are Marriott, Hilton, and Other.** + +# BEGIN SUBPROB + +First, Jasmine fits a linear model *without* an intercept term. Her prediction rule, $H_1$, looks like: + +$$H_{1}(x) = w_1 \cdot \texttt{price} + w_2 \cdot \texttt{is\_Marriott} + w_3 \cdot \texttt{is\_Hilton} + w_4 \cdot \texttt{is\_Other}$$ + +After fitting her model, $\vec{w}^* = \begin{bmatrix}−0.5 \\ 200 \\ 300 \\ 50 \end{bmatrix}$. + +1. The Marriott Marquis San Diego Marina, a hotel in the Marriott chain, has an average listing price of $250. How many open rooms does $H_1$ predict it has? Give your answer as a number with no variables. +2. The Marriott Marquis San Diego Marina actually has 45 open rooms. What’s the squared loss of your prediction above? Give your answer as a number with no variables. +3. True or False: Because your answer to (ii) above is not 0, it means there were no hotels in the Marriott chain with an average listing price of $250 in the training set. +( ) True +( ) False + +# BEGIN SOLUTION + +**Answers:** + +1. 75 +2. 900 +3. False + +If we plug in the weights from $\vec{w}^*$ into the equation for $H_1(x)$, noting that the values of the one-hot variables are either 0 or 1, we get $-0.5 \cdot 250 + 200 \cdot 1 + 300 \cdot 0 + 50 \cdot 0$, or $-125 + 200$, or 75. + +For part 2, the difference between predicted and actual number of rooms is $75 - 45 = 30$, and the squared loss is simply $30^2 = 900$. + +For part 3, the answer is False, since the fact that our best-fit line has an error at a given input does not mean that this input was not seen in the training data. In other words, the line of best fit does not always have to pass through all of the training points (and due to overfitting, in most cases you don't want it to). + +87 + +# END SOLUTION + +# END SUBPROB + +# BEGIN SUBPROB + +Then, on the same training set, Aritra fits a linear model, *with* an intercept term but without the `is_Other` feature. His new prediction rule, $H_2$, now looks like: + +$$H_2(x) = \beta_0 + \beta_1 \cdot \texttt{price} + \beta_2 \cdot \texttt{is\_Marriott} + \beta_3 \cdot \texttt{is\_Hilton}$$ + +After fitting his model, Aritra finds optimal coefficients $\beta_{0}^{*}$, $\beta_{1}^{*}$, $\beta_{2}^{*}$, and $\beta_{3}^{*}$. + +1. The training RMSE of $H_2$ is equal to the training RMSE of $H_1$. + +( ) True +( ) False + +2. Assuming we use the same test set, the test RMSE of $H_2$ is equal to the test RMSE of $H_1$. + +( ) True +( ) False + +# BEGIN SOLUTION + +**Answers:** + +1. True +2. True + +In model $H_1$, there is redundant information in the one-hot encoded features, creating multicollinearity. The second model $H_2$ removes the `is_Other` feature, but the intercept term it is replaced with serves a similar function. When `is_Other` is true, the prediction of $H_1$ is $w_1 \cdot \texttt{price} + w_4$, and the prediction of $H_2$ is $\beta_1 \cdot \texttt{price} + \beta_0$. The multicollinearity in $H_1$ doesn't affect model performance relative to model 2, but it will yield different parameter estimates since there will be multiple solutions, unlike with $H_2$. However, the models will have equivalent best solutions, even if the parameters differ, so both parts are True. + +53 + +# END SOLUTION + +# END SUBPROB + +# BEGIN SUBPROB + +After fitting his model, Aritra finds $\beta_{0}^{*} = 50.$ Given that, what are $\beta_{1}^{*}$, $\beta_{2}^{*}$, and $\beta_{3}^{*}$? Give your answers as numbers with no variables. + +# BEGIN SOLUTION + +**Answers:** + +1. -0.5 +2. 150 +3. 250 + +As we saw in the previous question, these models should yield an equivalent best-fit line. The relationship between `price` and predicted outcome will be the same, so $\beta_{1}^{*}$ will be $-0.5$, the same weight as in $H_1$. + +If $\beta_{0}^{*} = 50$, this means we are adding 50 to all predictions, and that the "adjustments" we make to the prediction for `is_Marriott` and `is_Hilton` should therefore be reduced to compensate for this; therefore, the new weights $\beta_{2}^{*}$ and $\beta_{3}^{*}$ will be 150 and 250. + +69 + +# END SOLUTION + +# END SUBPROB + +# END PROB \ No newline at end of file diff --git a/problems/wi24-final/wi24-final-q12.md b/problems/wi24-final/wi24-final-q12.md new file mode 100644 index 0000000..873763d --- /dev/null +++ b/problems/wi24-final/wi24-final-q12.md @@ -0,0 +1,102 @@ +# BEGIN PROB + +Diego also wants to build a model that predicts the number of open rooms a hotel has, given various other features. He has a training set with 1200 rows available to him for the purposes of training his model. + +# BEGIN SUBPROB + +Diego fits a regression model using the `GPTRegression` class. `GPTRegression` models have several hyperparameters that can be tuned, including `context_length` and `sentience`. + +To choose between 5 possible values of the hyperparameter `context_length`, Diego performs $k$-fold cross-validation. + +1. How many total times is a `GPTRegression` model fit? + +( ) $4k$ +( ) $5k$ +( ) $240k$ +( ) $6000k$ +( ) $4(k − 1)$ +( ) $5(k − 1)$ +( ) $240(k − 1)$ +( ) $6000(k − 1)$ + +2. Suppose that every time a `GPTRegression` model is fit, it appends the number of points in its training set to the list `sizes`. Note that after performing cross- validation, `len(sizes)` is equal to your answer to the previous subpart. + +What is `sum(sizes)`? + +( ) $4k$ +( ) $5k$ +( ) $240k$ +( ) $6000k$ +( ) $4(k − 1)$ +( ) $5(k − 1)$ +( ) $240(k − 1)$ +( ) $6000(k − 1)$ + +# BEGIN SOLUTION + +**Answers:** + +1. $5k$ +2. $6000(k-1)$ + +When we do $k$-fold cross-validation for one single hyperparameter value, we split the dataset into $k$ folds, and in each iteration $i$, train the model on the remaining $k-1$ folds and evaluate on fold $i$. Since every fold is left out and evaluated on once, the model is fit in total $k$ times. We do this once for every hyperparameter value we want to test, so the total number of model fits required is $5k$. + +In part 2, we can note that each model fit is performed on the same size of data -- the size of the remaining $k-1$ folds when we hold out a single fold. This size is $1 - \frac{1}{k} = \frac{k-1}{k}$ times the size of the entire dataset, in this case, $1200 \cdot \frac{k-1}{k}$, and we fit a model on a dataset of this size $5k$ times. So, the sum of the training sizes for each model fit is: + +$$5k \cdot \frac{k-1}{k} \cdot 1200 = 6000(k-1)$$ + +66 + +# END SOLUTION + +# END SUBPROB + +# BEGIN SUBPROB + +The average training error and validation error for all 5 candidate values of `context_length` are given below. + +
    + +Fill in the blanks: As `context_length` increases, model complexity `__(i)__`. The optimal choice of `context_length` is `__(ii)__`; if we choose a `context_length` any higher than that, our model will `__(iii)__`. + +1. What goes in blank (i)? + +( ) increases +( ) decreases + +2. What goes in blank (ii)? + +( ) 0.1 +( ) 1 +( ) 10 +( ) 100 +( ) 1000 + +3. What goes in blank (iii)? + +( ) overfit the training data and have high bias +( ) underfit the training data and have high bias +( ) overfit the training data and have low bias +( ) underfit the training data and have low bias + +# BEGIN SOLUTION + +**Answers:** + +1. decreases +2. 100 +3. underfit the training data and have high bias + +In part 1, we can see that as `context_length` increases, the training error increases, and the model performs worse. In general, higher model complexity leads to better model performance, so here, increasing `context_length` is *reducing* model complexity. + +In part 2, we will choose a `context_length` of 100, since this parameterization leads to the best validation performance. If we increase `context_length` further, the validation error increases. + +In part 3, since increased `context_length` indicates *less* complexity and worse training performance, increasing the `context_length` further would lead to underfitting, as the model would lack the expressiveness or number of parameters required to capture the data. Since training error represents model bias, and since high variance is associated with *over*fitting, a further increase in `context_length` would mean a more biased model. + +65 + +# END SOLUTION + +# END SUBPROB + +# END PROB From 2d2a4f1583f90eae617e0fb33e26809787f45147 Mon Sep 17 00:00:00 2001 From: Praveen Nair Date: Wed, 29 May 2024 15:20:42 -0700 Subject: [PATCH 2/2] Fixes to WI24 final --- docs/wi24-final/index.html | 41 ++++++++++++++++----- problems/wi24-final/wi24-final-data-info.md | 4 +- problems/wi24-final/wi24-final-q02.md | 2 +- problems/wi24-final/wi24-final-q04.md | 6 +-- problems/wi24-final/wi24-final-q06.md | 8 ++++ problems/wi24-final/wi24-final-q11.md | 9 +++++ 6 files changed, 54 insertions(+), 16 deletions(-) diff --git a/docs/wi24-final/index.html b/docs/wi24-final/index.html index 3e820bc..bb074b8 100644 --- a/docs/wi24-final/index.html +++ b/docs/wi24-final/index.html @@ -148,10 +148,10 @@

    Winter 2024 Final Exam

  • "Hotel Name" (str): The name of the hotel. Assume hotel names are unique.
  • "Location" (str): The hotel’s neighborhood in San -Diego
  • +Diego.
  • "Chain" (str): The chain the hotel is a part of; either "Hilton", "Marriott", "Hyatt", or "Other". A hotel chain is -a group of hotels owned or operated by a shared company
  • +a group of hotels owned or operated by a shared company.
  • "Number of Rooms" (int): The number of rooms the hotel has.
  • @@ -552,9 +552,12 @@

    -

    Answers: 1. permutation test 2. either the -(absolute) difference in means or the K-S statistic, depending on the -shapes of the observed distributions

    +

    Answers:

    +
      +
    1. permutation test
    2. +
    3. either the (absolute) difference in means or the K-S statistic, +depending on the shapes of the observed distributions
    4. +

    In part 1, we use a permutation test because we’re comparing two sampled distributions (the values of age for rows with missing vs. present values of is_business), rather than @@ -723,7 +726,7 @@

    one-tailed test, and since to reject the null hypothesis and provide some evidence towards the alternate hypothesis, the p-value should be lower, the alternate hypothesis should be the complement of -obs >= sum.

    +obs >= sm.

    For part 3, the answer is “all primary occupants” because our sampling procedure doesn’t sample just from (full or partial) business travelers, but from the entire DataFrame. (In the line where we sample, @@ -972,11 +975,11 @@

    Difficulty: ⭐️⭐️⭐️


    Problem 4.3

    Fill in blanks (i) and (ii) in site so that the -following all evaluate to True:

    +following all evaluate to True:

      -
    • len(site.find all("div", class ="chain")) == 2
    • +
    • len(site.find_all("div", class_ ="chain")) == 2
    • chain_color("Hyatt") == "purple"
    • -
    • site.find all("div")[-1].text == ""
    • +
    • site.find_all("div")[-1].text == ""
    1. What goes in blank (i)?
    2. @@ -1200,6 +1203,15 @@

      Problem 6.2

      \frac{9}{10}, when using a base-2 logarithm to compute the IDF. How many of the reviews on TripAdvisor for this hotel contain the term "beach"?

      +
        +
      • 3

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      @@ -1763,7 +1775,7 @@

      Problem 11.1

      number with no variables.
    3. True or False: Because your answer to (ii) above is not 0, it means there were no hotels in the Marriott chain with an average listing price -of $250 in the training set. ( ) True ( ) False
    4. +of $250 in the training set. d ( ) True ( ) False
    @@ -1877,6 +1889,15 @@
    Difficulty: ⭐️⭐️⭐️


    Problem 11.3

    +

    As a reminder,

    +

    H_{1}(x) = w_1 \cdot \texttt{price} + w_2 +\cdot \texttt{is\_Marriott} + w_3 \cdot \texttt{is\_Hilton} + w_4 \cdot +\texttt{is\_Other}

    +

    \vec{w}^* = \begin{bmatrix}−0.5 \\ 200 \\ +300 \\ 50 \end{bmatrix}

    +

    H_2(x) = \beta_0 + \beta_1 \cdot +\texttt{price} + \beta_2 \cdot \texttt{is\_Marriott} + \beta_3 \cdot +\texttt{is\_Hilton}

    After fitting his model, Aritra finds \beta_{0}^{*} = 50. Given that, what are \beta_{1}^{*}, = sum`. +For part 2, the samples capture how likely the deviation of the observed statistic is to happen under the null hypothesis, but the p-value is being calculated by adding up whenever the observed statistic is greater or equal to the sample. This indicates that we're doing a one-tailed test, and since to reject the null hypothesis and provide some evidence towards the alternate hypothesis, the p-value should be lower, the alternate hypothesis should be the complement of `obs >= sm`. For part 3, the answer is "all primary occupants" because our sampling procedure doesn't sample just from (full or partial) business travelers, but from the entire DataFrame. (In the line where we sample, the only arguments are the number of rows we're sampling, and that we're doing so without replacement -- nothing about restricting which rows in `guest` to sample.) In other words, we're not comparing primary occupants not on business trips to those on business trips, but rather we're comparing primary occupants to the entire dataset of occupants. diff --git a/problems/wi24-final/wi24-final-q04.md b/problems/wi24-final/wi24-final-q04.md index 343fdd2..f7b41cc 100644 --- a/problems/wi24-final/wi24-final-q04.md +++ b/problems/wi24-final/wi24-final-q04.md @@ -57,11 +57,11 @@ The solution finds all `div` elements whose `name` attribute is equal to the fun # BEGIN SUBPROB -Fill in blanks (i) and (ii) in `site` so that the following all evaluate to True: +Fill in blanks (i) and (ii) in `site` so that the following all evaluate to `True`: -- `len(site.find all("div", class ="chain")) == 2` +- `len(site.find_all("div", class_ ="chain")) == 2` - `chain_color("Hyatt") == "purple"` -- `site.find all("div")[-1].text == ""` +- `site.find_all("div")[-1].text == ""` 1. What goes in blank (i)? 2. What goes in blank (ii)? diff --git a/problems/wi24-final/wi24-final-q06.md b/problems/wi24-final/wi24-final-q06.md index cbf1e85..d643bde 100644 --- a/problems/wi24-final/wi24-final-q06.md +++ b/problems/wi24-final/wi24-final-q06.md @@ -26,6 +26,14 @@ The answer is simply the proportion of words in the sentence that are the word ` The TF-IDF of `"beach"` in Gabriel’s favorite review is $\frac{9}{10}$, when using a base-2 logarithm to compute the IDF. How many of the reviews on TripAdvisor for this hotel contain the term `"beach"`? +( ) 3 +( ) 6 +( ) 8 +( ) 12 +( ) 16 +( ) 24 +( ) 32 + # BEGIN SOLUTION **Answer:** 12 diff --git a/problems/wi24-final/wi24-final-q11.md b/problems/wi24-final/wi24-final-q11.md index 8fd292d..14c233d 100644 --- a/problems/wi24-final/wi24-final-q11.md +++ b/problems/wi24-final/wi24-final-q11.md @@ -13,6 +13,7 @@ After fitting her model, $\vec{w}^* = \begin{bmatrix}−0.5 \\ 200 \\ 300 \\ 50 1. The Marriott Marquis San Diego Marina, a hotel in the Marriott chain, has an average listing price of $250. How many open rooms does $H_1$ predict it has? Give your answer as a number with no variables. 2. The Marriott Marquis San Diego Marina actually has 45 open rooms. What’s the squared loss of your prediction above? Give your answer as a number with no variables. 3. True or False: Because your answer to (ii) above is not 0, it means there were no hotels in the Marriott chain with an average listing price of $250 in the training set. + d ( ) True ( ) False @@ -71,6 +72,14 @@ In model $H_1$, there is redundant information in the one-hot encoded features, # BEGIN SUBPROB +As a reminder, + +$$H_{1}(x) = w_1 \cdot \texttt{price} + w_2 \cdot \texttt{is\_Marriott} + w_3 \cdot \texttt{is\_Hilton} + w_4 \cdot \texttt{is\_Other}$$ + +$$\vec{w}^* = \begin{bmatrix}−0.5 \\ 200 \\ 300 \\ 50 \end{bmatrix}$$ + +$$H_2(x) = \beta_0 + \beta_1 \cdot \texttt{price} + \beta_2 \cdot \texttt{is\_Marriott} + \beta_3 \cdot \texttt{is\_Hilton}$$ + After fitting his model, Aritra finds $\beta_{0}^{*} = 50.$ Given that, what are $\beta_{1}^{*}$, $\beta_{2}^{*}$, and $\beta_{3}^{*}$? Give your answers as numbers with no variables. # BEGIN SOLUTION

    Winter 2024 Suraj RampureMidterm 🆕 + Midterm +
    + Final 🆕
    Sam Lau Midterm
    - Final 🆕 + Final
    Spring 2023 Tauhidur Rahman - Final 🆕 + Final
    Suraj Rampure Midterm
    - Final 🆕 + Final

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