diff --git a/constant_model_loss_transformations/images/constant_loss_surface.png b/constant_model_loss_transformations/images/constant_loss_surface.png new file mode 100644 index 00000000..1cd733bd Binary files /dev/null and b/constant_model_loss_transformations/images/constant_loss_surface.png differ diff --git a/constant_model_loss_transformations/images/dugong_rug.png b/constant_model_loss_transformations/images/dugong_rug.png new file mode 100644 index 00000000..9c5e9df6 Binary files /dev/null and b/constant_model_loss_transformations/images/dugong_rug.png differ diff --git a/constant_model_loss_transformations/images/dugong_scatter.png b/constant_model_loss_transformations/images/dugong_scatter.png new file mode 100644 index 00000000..4bf3a8b0 Binary files /dev/null and b/constant_model_loss_transformations/images/dugong_scatter.png differ diff --git a/constant_model_loss_transformations/images/mae_loss.png b/constant_model_loss_transformations/images/mae_loss.png new file mode 100644 index 00000000..bb8a7f4d Binary files /dev/null and b/constant_model_loss_transformations/images/mae_loss.png differ diff --git a/constant_model_loss_transformations/images/mse_loss.png b/constant_model_loss_transformations/images/mse_loss.png new file mode 100644 index 00000000..51f8aa55 Binary files /dev/null and b/constant_model_loss_transformations/images/mse_loss.png differ diff --git a/constant_model_loss_transformations/images/slr_loss_surface.png b/constant_model_loss_transformations/images/slr_loss_surface.png new file mode 100644 index 00000000..66320e5d Binary files /dev/null and b/constant_model_loss_transformations/images/slr_loss_surface.png differ diff --git a/constant_model_loss_transformations/images/slr_modeling_process.png b/constant_model_loss_transformations/images/slr_modeling_process.png new file mode 100644 index 00000000..45b5e974 Binary files /dev/null and b/constant_model_loss_transformations/images/slr_modeling_process.png differ diff --git a/constant_model_loss_transformations/loss_transformations.ipynb b/constant_model_loss_transformations/loss_transformations.ipynb new file mode 100644 index 00000000..c248ffdd --- /dev/null +++ b/constant_model_loss_transformations/loss_transformations.ipynb @@ -0,0 +1,952 @@ +{ + "cells": [ + { + "cell_type": "raw", + "metadata": {}, + "source": [ + "---\n", + "title: 'Constant Model, Loss, and Transformations'\n", + "execute:\n", + " echo: true\n", + "format:\n", + " html:\n", + " code-fold: true\n", + " code-tools: true\n", + " toc: true\n", + " toc-title: 'Constant Model, Loss, and Transformations'\n", + " page-layout: full\n", + " theme:\n", + " - cosmo\n", + " - cerulean\n", + " callout-icon: false\n", + "---" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "::: {.callout-note collapse=\"true\"}\n", + "## Learning Outcomes\n", + "* Derive the optimal model parameters for the constant model under MSE and MAE cost functions\n", + "* Evaluate the differences between MSE and MAE risk\n", + "* Understand the need for linearization of variables and apply the Tukey-Mosteller bulge diagram for transformations\n", + ":::\n", + "\n", + "Last time, we introduced the modeling process. We set up a framework to predict target variables as functions of our features, following a set workflow:\n", + "\n", + "1. Choose a model - how should we represent the world? \n", + "2. Choose a loss function - how do we quantify prediction error? \n", + "3. Fit the model - how do we choose the best parameter of our model given our data? \n", + "4. Evaluate model performance - how do we evaluate whether this process gave rise to a good model? \n", + "\n", + "To illustrate this process, we derived the optimal model parameters under simple linear regression (SLR) with mean squared error (MSE) as the cost function. A summary of the SLR modeling process is shown below: \n", + "\n", + "
\n", + "error\n", + "
\n", + "\n", + "In this lecture, we'll dive deeper into step 4 - evaluating model performance - using SLR as an example. Additionally, we'll also explore the modeling process with new models continue familiarizing ourselves with the modeling process by finding the best model parameters under a new model, the constant model, and test out two different loss functions to understand how our choice of loss influences model design. Later on, we'll consider what happens when a linear model isn't the best choice to capture trends in our data and what solutions there are to create better models." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 4: Evaluating the SLR Model\n", + "Now that we've explored the mathematics behind (1) choosing a model, (2) choosing a loss function, and (3) fitting the model, we're left with one final question – how \"good\" are the predictions made by this \"best\" fitted model? To determine this, we can: \n", + "\n", + "1. Visualize data and compute statistics: \n", + " * Plot the original data.\n", + " * Compute each column's mean and standard deviation. If the mean and standard deviation of our predictions are close to those of the original observed $y_i$s, we might be inclined to say that our model has done well.\n", + " * (if we're fitting a linear model) compute the correlation $r$. A large magnitude for the correlation coefficient between the feature and response variables could also indicate that our model has done well.\n", + "2. Performance metrics: \n", + " * We can take the **root mean squared error (RMSE)**\n", + " * It's the square root of the mean squared error (MSE), which is the average loss that we've been minimizing to determine optimal model parameters.\n", + " * RMSE is in the same unis as $y$.\n", + " * A lower RMSE indicates more \"accurate\" predictions, as we have a lower \"average loss\" across the data.\n", + "\n", + " $$\\text{RMSE} = \\sqrt{\\frac{1}{n} \\sum_{i=1}^n (y_i - \\hat{y}_i)^2}$$\n", + " \n", + "3. Visualization: \n", + " * look at the residual plot of $e_i = y_i - \\hat{y_i}$ to visualize the difference between actual and predicted values.\n", + "\n", + "To illustrate this process, let's take a look at **Anscombe's quartet**. \n", + "\n", + "### Four Mysterious Datasets (Anscombe’s quartet)\n", + "Let's take look at four different datasets. " + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "#| code-fold: true\n", + "import numpy as np\n", + "import pandas as pd\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "import seaborn as sns\n", + "import itertools\n", + "from mpl_toolkits.mplot3d import Axes3D" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "#| code-fold: true\n", + "# Big font helper\n", + "def adjust_fontsize(size=None):\n", + " SMALL_SIZE = 8\n", + " MEDIUM_SIZE = 10\n", + " BIGGER_SIZE = 12\n", + " if size != None:\n", + " SMALL_SIZE = MEDIUM_SIZE = BIGGER_SIZE = size\n", + "\n", + " plt.rc('font', size=SMALL_SIZE) # controls default text sizes\n", + " plt.rc('axes', titlesize=SMALL_SIZE) # fontsize of the axes title\n", + " plt.rc('axes', labelsize=MEDIUM_SIZE) # fontsize of the x and y labels\n", + " plt.rc('xtick', labelsize=SMALL_SIZE) # fontsize of the tick labels\n", + " plt.rc('ytick', labelsize=SMALL_SIZE) # fontsize of the tick labels\n", + " plt.rc('legend', fontsize=SMALL_SIZE) # legend fontsize\n", + " plt.rc('figure', titlesize=BIGGER_SIZE) # fontsize of the figure title\n", + "\n", + "# Helper functions\n", + "def standard_units(x):\n", + " return (x - np.mean(x)) / np.std(x)\n", + "\n", + "def correlation(x, y):\n", + " return np.mean(standard_units(x) * standard_units(y))\n", + "\n", + "def slope(x, y):\n", + " return correlation(x, y) * np.std(y) / np.std(x)\n", + "\n", + "def intercept(x, y):\n", + " return np.mean(y) - slope(x, y)*np.mean(x)\n", + "\n", + "def fit_least_squares(x, y):\n", + " theta_0 = intercept(x, y)\n", + " theta_1 = slope(x, y)\n", + " return theta_0, theta_1\n", + "\n", + "def predict(x, theta_0, theta_1):\n", + " return theta_0 + theta_1*x\n", + "\n", + "def compute_mse(y, yhat):\n", + " return np.mean((y - yhat)**2)\n", + "\n", + "plt.style.use('default') # Revert style to default mpl" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#| code-fold: true\n", + "# Load in four different datasets: I, II, III, IV\n", + "x = [10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5]\n", + "y1 = [8.04, 6.95, 7.58, 8.81, 8.33, 9.96, 7.24, 4.26, 10.84, 4.82, 5.68]\n", + "y2 = [9.14, 8.14, 8.74, 8.77, 9.26, 8.10, 6.13, 3.10, 9.13, 7.26, 4.74]\n", + "y3 = [7.46, 6.77, 12.74, 7.11, 7.81, 8.84, 6.08, 5.39, 8.15, 6.42, 5.73]\n", + "x4 = [8, 8, 8, 8, 8, 8, 8, 19, 8, 8, 8]\n", + "y4 = [6.58, 5.76, 7.71, 8.84, 8.47, 7.04, 5.25, 12.50, 5.56, 7.91, 6.89]\n", + "\n", + "anscombe = {\n", + " 'I': pd.DataFrame(list(zip(x, y1)), columns =['x', 'y']),\n", + " 'II': pd.DataFrame(list(zip(x, y2)), columns =['x', 'y']),\n", + " 'III': pd.DataFrame(list(zip(x, y3)), columns =['x', 'y']),\n", + " 'IV': pd.DataFrame(list(zip(x4, y4)), columns =['x', 'y'])\n", + "}\n", + "\n", + "# Plot the scatter plot and line of best fit \n", + "fig, axs = plt.subplots(2, 2, figsize = (10, 10))\n", + "\n", + "for i, dataset in enumerate(['I', 'II', 'III', 'IV']):\n", + " ans = anscombe[dataset]\n", + " x, y = ans['x'], ans['y']\n", + " ahat, bhat = fit_least_squares(x, y)\n", + " yhat = predict(x, ahat, bhat)\n", + " axs[i//2, i%2].scatter(x, y, alpha=0.6, color='red') # plot the x, y points\n", + " axs[i//2, i%2].plot(x, yhat) # plot the line of best fit \n", + " axs[i//2, i%2].set_xlabel(f'$x_{i+1}$')\n", + " axs[i//2, i%2].set_ylabel(f'$y_{i+1}$')\n", + " axs[i//2, i%2].set_title(f\"Dataset {dataset}\")\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "While these four sets of points look very different, they actually all have identical $\\bar x$, $\\bar y$, $\\sigma_x$, $\\sigma_y$, correlation $r$, and RMSE! If we only look at these statistics, we will probably be inclined to say that these datasets are similar." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + ">>> Dataset I:\n", + "x_mean : 9.00, y_mean : 7.50\n", + "x_stdev: 3.16, y_stdev: 1.94\n", + "r = Correlation(x, y): 0.816\n", + "\theta_0: 3.00, \theta_1: 0.50\n", + "RMSE: 1.119\n", + "\n", + "\n", + ">>> Dataset II:\n", + "x_mean : 9.00, y_mean : 7.50\n", + "x_stdev: 3.16, y_stdev: 1.94\n", + "r = Correlation(x, y): 0.816\n", + "\theta_0: 3.00, \theta_1: 0.50\n", + "RMSE: 1.119\n", + "\n", + "\n", + ">>> Dataset III:\n", + "x_mean : 9.00, y_mean : 7.50\n", + "x_stdev: 3.16, y_stdev: 1.94\n", + "r = Correlation(x, y): 0.816\n", + "\theta_0: 3.00, \theta_1: 0.50\n", + "RMSE: 1.118\n", + "\n", + "\n", + ">>> Dataset IV:\n", + "x_mean : 9.00, y_mean : 7.50\n", + "x_stdev: 3.16, y_stdev: 1.94\n", + "r = Correlation(x, y): 0.817\n", + "\theta_0: 3.00, \theta_1: 0.50\n", + "RMSE: 1.118\n", + "\n", + "\n" + ] + } + ], + "source": [ + "#| code-fold: true\n", + "for dataset in ['I', 'II', 'III', 'IV']:\n", + " print(f\">>> Dataset {dataset}:\")\n", + " ans = anscombe[dataset]\n", + " fig = least_squares_evaluation(ans['x'], ans['y'], visualize = NO_VIZ)\n", + " print()\n", + " print()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We may also wish to visualize the model's **residuals**, defined as the difference between the observed and predicted $y_i$ value ($e_i = y_i - \\hat{y}_i$). This gives a high-level view of how \"off\" each prediction is from the true observed value. Recall that you explored this concept in [Data 8](https://inferentialthinking.com/chapters/15/5/Visual_Diagnostics.html?highlight=heteroscedasticity#detecting-heteroscedasticity): a good regression fit should display no clear pattern in its plot of residuals. The residual plots for Anscombe's quartet are displayed below. Note how only the first plot shows no clear pattern to the magnitude of residuals. This is an indication that SLR is not the best choice of model for the remaining three sets of points.\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#| code-fold: true\n", + "# residual visualization\n", + "fig, axs = plt.subplots(2, 2, figsize = (10, 10))\n", + "\n", + "for i, dataset in enumerate(['I', 'II', 'III', 'IV']):\n", + " ans = anscombe[dataset]\n", + " x, y = ans['x'], ans['y']\n", + " ahat, bhat = fit_least_squares(x, y)\n", + " yhat = predict(x, ahat, bhat)\n", + " axs[i//2, i%2].scatter(x, y - yhat, alpha=0.6, color='red') # plot the x, y points\n", + " axs[i//2, i%2].plot(x, np.zeros_like(x), color='black') # plot the residual line\n", + " axs[i//2, i%2].set_xlabel(f'$x_{i+1}$')\n", + " axs[i//2, i%2].set_ylabel(f'$e_{i+1}$')\n", + " axs[i//2, i%2].set_title(f\"Dataset {dataset} Residuals\")\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Prediction vs. Estimation\n", + "The terms prediction and estimation are often used somewhat interchangeably, but there is a subtle difference between them. **Estimation** is the task of using data to calculate model parameters. **Prediction** is the task of using a model to predict outputs for unseen data. In our simple linear regression model \n", + "\n", + "$$\\hat{y} = \\hat{\\theta_0} + \\hat{\\theta_1}$$\n", + "\n", + "we **estimate** the parameters by minimizing average loss; then, we **predict** using these estimations. **Least Squares Estimation** is when we choose the parameters that minimize MSE." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Constant Model + MSE\n", + "\n", + "Now, we'll shift from the SLR model to the **constant model**, also known as a summary statistic. The constant model is slightly different from the simple linear regression model we've explored previously. Rather than generate predictions from an inputted feature variable, the constant model always *predicts the same constant number.* This ignores any relationships between variables. For example, let's say we want to predict the number of drinks a boba shop sells in a day. Boba tea sales likely depend on the time of year, the weather, how the customers feel, whether school is in session, etc, but the constant model ignores these factors in favor of a simpler model. In other words, the constant model employs a **simplifying assumption**. \n", + "\n", + "It is also a parametric, statistical mode\n", + "\n", + "$$\\hat{y}_i = \\theta_0$$\n", + "\n", + "$\\theta_0$ is the parameter of the constant model, just as $\\theta_0$ and $\\theta_1$ were the parameters in SLR. \n", + "Since our parameter $\\theta_0$ is 1-dimensional ($\\theta_0 \\in \\mathbb{R}$), we now have no input to our model and will always predict $\\hat{y}_i = \\theta_0$.\n", + "\n", + "### Deriving the optimal $\\theta_0$\n", + "Our task now is to determine what value of $\\theta_0$ best represents the optimal model – in other words, what number should we guess each time to have the lowest possible **average loss** on our data?\n", + "\n", + "Like before, we'll use Mean Squared Error (MSE). Recall that the MSE is average squared loss (L2 loss) over the data $D = \\{y_1, y_2, ..., y_n\\}$.\n", + "\n", + "$$R(\\theta) = \\frac{1}{n}\\sum^{n}_{i=1} (y_i - \\hat{y_i})^2 $$\n", + "\n", + "Our modeling process now looks like this: \n", + "\n", + "1. Choose a model: constant model\n", + "2. Choose a loss function: L1 loss\n", + "3. Fit the model\n", + "4. Evaluate model performance\n", + "\n", + "\n", + "Given the **constant model** $\\hat{y}_i = \\theta_0$, we can rewrite the MSE equation as \n", + "\n", + "$$R(\\theta) = \\frac{1}{n}\\sum^{n}_{i=1} (y_i - \\theta_0)^2 $$\n", + "\n", + "We can fit **the model** by finding the optimal $\\theta_0$ that minimizes the MSE using a calculus approach. \n", + "\n", + "1. Differentiate with respect to $\\theta_0$\n", + "\n", + "$$\n", + "\\begin{align}\n", + "\\frac{d}{d\\theta_0}\\text{R}(\\theta) & = \\frac{d}{d\\theta_0}\\frac{1}{n}\\sum^{n}_{i=1} (y_i - \\theta_0)^2\n", + "\\\\ &= {n}\\sum^{n}_{i=1} \\frac{d}{d\\theta_0} (y_i - \\theta_0)^2 \\quad \\quad \\text{derivative of sum is a sum of derivatives}\n", + "\\\\ &= {n}\\sum^{n}_{i=1} 2 (y_i - \\theta_0) (-1) \\quad \\quad \\text{chain rule}\n", + "\\\\ &= {\\frac{-2}{n}}\\sum^{n}_{i=1} (y_i - \\theta_0) \\quad \\quad \\text{simply constants}\n", + "\\end{align}\n", + "$$\n", + "\n", + "2. Set equal to 0\n", + "$$\n", + "0 = {\\frac{-2}{n}}\\sum^{n}_{i=1} (y_i - \\theta_0)\n", + "$$\n", + "\n", + "3. Solve for $\\theta_0$\n", + "\n", + "$$\n", + "\\begin{align}\n", + "0 &= {\\frac{-2}{n}}\\sum^{n}_{i=1} (y_i - \\theta_0)\n", + "\\\\ &= \\sum^{n}_{i=1} (y_i - \\theta_0) \\quad \\quad \\text{divide both sides by} \\frac{-2}{n} \n", + "\\\\ &= \\sum^{n}_{i=1} y_i - \\sum^{n}_{i=1} \\theta_0 \\quad \\quad \\text{separate sums}\n", + "\\\\ &= \\sum^{n}_{i=1} y_i - n * \\theta_0 \\quad \\quad \\text{c + c + … + c = nc}\n", + "\\\\ n * \\theta_0 &= \\sum^{n}_{i=1} y_i \n", + "\\\\ \\theta_0 &= \\frac{1}{n} \\sum^{n}_{i=1} y_i \n", + "\\\\ \\theta_0 &= \\bar{y}\n", + "\\end{align}\n", + "$$\n", + "\n", + "Let's take a moment to interpret this result. $\\hat{\\theta} = \\bar{y}$ is the optimal parameter for constant model + MSE.\n", + "It holds true regardless of what data sample you have, and it provides some formal reasoning as to why the mean is such a common summary statistic.\n", + "\n", + "Our optimal model parameter is the value of the parameter that minimizes the cost function. This minimum value of the cost function can be expressed:\n", + "\n", + "$$R(\\hat{\\theta}) = \\min_{\\theta} R(\\theta)$$\n", + "\n", + "To restate the above in plain English: we are looking at the value of the cost function when it takes the best parameter as input. This optimal model parameter, $\\hat{\\theta}$, is the value of $\\theta$ that minimizes the cost $R$.\n", + "\n", + "For modeling purposes, we care less about the minimum value of cost, $R(\\hat{\\theta})$, and more about the *value of $\\theta$* that results in this lowest average loss. In other words, we concern ourselves with finding the best parameter value such that:\n", + "\n", + "$$\\hat{\\theta} = \\underset{\\theta}{\\operatorname{\\arg\\min}}\\:R(\\theta)$$\n", + "\n", + "That is, we want to find the **arg**ument $\\theta$ that **min**imizes the cost function." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Comparing Two Different Models, Both Fit with MSE\n", + "Now that we've explored the constant model with an L2 loss, we can compare it to the SLR model that we learned last lecture. Consider the dataset below, which contains information about the ages and lengths of dugongs. Supposed we wanted to predict dugong ages:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "| | Constant Model | Simple Linear Regression |\n", + "| -- | -------------- | ------------------------ |\n", + "| model | $\\hat{y} = \\theta_0$ | $\\hat{y} = \\theta_0 + \\theta1 x$ |\n", + "| data | sample of ages $D = \\{y_1, y_2, ..., y_m\\}$ | sample of ages $D = \\{(x_1, y_1), (x_2, y_2), ..., (x_n, y_n)\\}$ |\n", + "| dimensions | $\\hat{\\theta_0}$ is 1-D | $\\hat{\\theta} = [\\hat{\\theta_0}, \\hat{\\theta_1}]$ is 2-D |\n", + "| loss surface | 2-D ![](images/constant_loss_surface.png) | 3-D ![](images/slr_loss_surface.png) | \n", + "| Loss Model | $R(\\theta) = \\frac{1}{n}\\sum^{n}_{i=1} (y_i - \\theta_0)^2 $ | $R(\\theta) = \\frac{1}{n}\\sum^{n}_{i=1} (y_i - (\\theta_0 + \\theta_1 x))^2 $ |\n", + "| RMSE | 7.72 | 4.31 |\n", + "| predictions visualized | rug plot ![](images/dugong_rug.png) | scatter plot ![](images/dugong_scatter.png) (notice how the points are visually not a great linear fit. We'll come back to this)|\n", + "\n", + "The code for generating the graphs and models are hidden below, but we won't go over it in too much depth" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#| code-fold: true\n", + "dugongs = pd.read_csv(\"data/dugongs.csv\")\n", + "data_constant = dugongs[\"Age\"]\n", + "data_linear = dugongs[[\"Length\", \"Age\"]]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#| code-fold: true\n", + "# Constant Model + MSE\n", + "plt.style.use('default') # Revert style to default mpl\n", + "adjust_fontsize(size=16)\n", + "%matplotlib inline\n", + "\n", + "def mse_constant(theta, data):\n", + " return np.mean(np.array([(y_obs - theta) ** 2 for y_obs in data]), axis=0)\n", + "\n", + "thetas = np.linspace(-20, 42, 1000)\n", + "l2_loss_thetas = mse_constant(thetas, data_constant)\n", + "\n", + "# plotting the loss surface\n", + "plt.plot(thetas, l2_loss_thetas)\n", + "plt.xlabel(r'$\\theta_0$')\n", + "plt.ylabel(r'MSE')\n", + "\n", + "# Optimal point\n", + "thetahat = np.mean(data_constant)\n", + "plt.scatter([thetahat], [mse_constant(thetahat, data_constant)], s=50, label = r\"$\\hat{\\theta}_0$\")\n", + "plt.legend()\n", + "# plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#| code-fold: true\n", + "# SLR + MSE\n", + "def mse_linear(theta_0, theta_1, data_linear):\n", + " data_x, data_y = data_linear.iloc[:,0], data_linear.iloc[:,1]\n", + " return np.mean(np.array([(y - (theta_0+theta_1*x)) ** 2 for x, y in zip(data_x, data_y)]), axis=0)\n", + "\n", + "# plotting the loss surface\n", + "theta_0_values = np.linspace(-80, 20, 80)\n", + "theta_1_values = np.linspace(-10, 30, 80)\n", + "mse_values = np.array([[mse_linear(x,y,data_linear) for x in theta_0_values] for y in theta_1_values])\n", + "\n", + "# Optimal point\n", + "data_x, data_y = data_linear.iloc[:, 0], data_linear.iloc[:, 1]\n", + "theta_1_hat = np.corrcoef(data_x, data_y)[0, 1] * np.std(data_y) / np.std(data_x)\n", + "theta_0_hat = np.mean(data_y) - theta_1_hat * np.mean(data_x)\n", + "\n", + "# Create the 3D plot\n", + "fig = plt.figure(figsize=(7, 5))\n", + "ax = fig.add_subplot(111, projection='3d')\n", + "\n", + "X, Y = np.meshgrid(theta_0_values, theta_1_values)\n", + "surf = ax.plot_surface(X, Y, mse_values, cmap='viridis', alpha=0.6) # Use alpha to make it slightly transparent\n", + "\n", + "# Scatter point using matplotlib\n", + "sc = ax.scatter([theta_0_hat], [theta_1_hat], [mse_linear(theta_0_hat, theta_1_hat, data_linear)],\n", + " marker='o', color='red', s=100, label='theta hat')\n", + "\n", + "# Create a colorbar\n", + "cbar = fig.colorbar(surf, ax=ax, shrink=0.5, aspect=10)\n", + "cbar.set_label('Cost Value')\n", + "\n", + "ax.set_title('MSE for different $\\\\theta_0, \\\\theta_1$')\n", + "ax.set_xlabel('$\\\\theta_0$')\n", + "ax.set_ylabel('$\\\\theta_1$') \n", + "ax.set_zlabel('MSE')\n", + "\n", + "# plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#| code-fold: true\n", + "# predictions\n", + "yobs = data_linear[\"Age\"] # The true observations y\n", + "xs = data_linear[\"Length\"] # Needed for linear predictions\n", + "n = len(yobs) # Predictions\n", + "\n", + "yhats_constant = [thetahat for i in range(n)] # Not used, but food for thought\n", + "yhats_linear = [theta_0_hat + theta_1_hat * x for x in xs]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#| code-fold: true\n", + "# Constant Model Rug Plot\n", + "# In case we're in a weird style state\n", + "sns.set_theme()\n", + "adjust_fontsize(size=16)\n", + "%matplotlib inline\n", + "\n", + "fig = plt.figure(figsize=(8, 1.5))\n", + "sns.rugplot(yobs, height=0.25, lw=2) ;\n", + "plt.axvline(thetahat, color='red', lw=4, label=r\"$\\hat{\\theta}_0$\");\n", + "plt.legend()\n", + "plt.yticks([])\n", + "# plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#| code-fold: true\n", + "# SLR model scatter plot \n", + "# In case we're in a weird style state\n", + "sns.set_theme()\n", + "adjust_fontsize(size=16)\n", + "%matplotlib inline\n", + "\n", + "sns.scatterplot(x=xs, y=yobs)\n", + "plt.plot(xs, yhats_linear, color='red', lw=4)\n", + "# plt.savefig('dugong_line.png', bbox_inches = 'tight');\n", + "# plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Interpreting the RMSE (Root Mean Squared Error):\n", + "* The constant error is HIGHER than the linear error. Hence,\n", + "* The constant model is WORSE than the linear model (at least for this metric)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Constant Model + MAE \n", + "\n", + "We see now that changing the model used for prediction leads to a wildly different result for the optimal model parameter. What happens if we instead change the loss function used in model evaluation?\n", + "\n", + "This time, we will consider the constant model with L1 (absolute loss) as the loss function. This means that the average loss will be expressed as the **Mean Absolute Error (MAE)**. \n", + "\n", + "1. Choose a model: constant model\n", + "2. Choose a loss function: L1 loss\n", + "3. Fit the model\n", + "4. Evaluate model performance\n", + "\n", + "### Deriving the optimal $\\theta_0$\n", + "\n", + "Recall that the **MAE** is average **absolute** loss (L1 loss) over the data $D = \\{y_1, y_2, ..., y_m\\}$.\n", + "\n", + "$$R(\\theta) = \\frac{1}{n}\\sum^{n}_{i=1} |y_i - \\hat{y_i}| $$\n", + "\n", + "Given the constant model $\\hat{y} = \\theta_0$, we can write the MAE as \n", + "\n", + "$$R(\\theta) = \\frac{1}{n}\\sum^{n}_{i=1} |y_i - \\theta_0| $$\n", + "\n", + "To fit the model, we find the optimal parameter value $\\hat{\\theta}$ by differentiating using a calculus approach:\n", + "\n", + "1. Differentiate with respect to $\\theta_0$.\n", + "\n", + "$$\n", + "R(\\theta) = \\frac{1}{n}\\sum^{n}_{i=1} |y_i - \\theta| \\\\\n", + "\\frac{d}{d\\theta} R(\\theta) = \\frac{d}{d\\theta} \\left(\\frac{1}{n} \\sum^{n}_{i=1} |y_i - \\theta| \\right) \\\\\n", + "\\frac{d}{d\\theta} R(\\theta) = \\frac{1}{n} \\sum^{n}_{i=1} \\frac{d}{d\\theta} |y_i - \\theta|\n", + "$$\n", + "\n", + "* Here, we seem to have run into a problem: the derivative of an absolute value is undefined when the argument is 0 (i.e. when $y_i = \\theta$). For now, we'll ignore this issue. It turns out that disregarding this case doesn't influence our final result.\n", + "* To perform the derivative, consider two cases. When $\\theta$ is *less than* $y_i$, the term $y_i - \\theta$ will be positive and the absolute value has no impact. When $\\theta$ is *greater than* $y_i$, the term $y_i - \\theta$ will be negative. Applying the absolute value will convert this to a positive value, which we can express by saying $-(y_i - \\theta) = \\theta - y_i$. \n", + "\n", + "$$|y_i - \\theta| = \\begin{cases} y_i - \\theta \\quad \\text{ if: } \\theta < y_i \\\\ \\theta - y_i \\quad \\text{if: }\\theta > y_i \\end{cases}$$\n", + "\n", + "* Taking derivatives:\n", + "\n", + "$$\\frac{d}{d\\theta} |y_i - \\theta| = \\begin{cases} \\frac{d}{d\\theta} (y_i - \\theta) = -1 \\quad \\text{if: }\\theta < y_i \\\\ \\frac{d}{d\\theta} (\\theta - y_i) = 1 \\quad \\text{if: }\\theta > y_i \\end{cases}$$\n", + "\n", + "* This means that we obtain a different value for the derivative for data points where $\\theta < y_i$ and where $\\theta > y_i$. We can summarize this by saying:\n", + "\n", + "$$\\frac{d}{d\\theta} R(\\theta) = \\frac{1}{n} \\sum^{n}_{i=1} \\frac{d}{d\\theta} |y_i - \\theta| \\\\\n", + "= \\frac{1}{n} \\left[\\sum_{\\hat{\\theta_0} < y_i} (-1) + \\sum_{\\hat{\\theta_0} > y_i} (+1) \\right]\n", + "$$\n", + "\n", + "* In other words, we take the sum of values for $i = 1, 2, ..., n$:\n", + " * $-1$ if our observation $y_i$ is *greater than* our prediction $\\hat{\\theta_0}$\n", + " * $+1$ if our observation $y_i$ is *smaller than* our prediction $\\hat{\\theta_0}$\n", + "\n", + "2. Set equal to 0. \n", + "$$ 0 = \\frac{1}{n}\\sum_{\\hat{\\theta_0} < y_i} (-1) + \\frac{1}{n}\\sum_{\\hat{\\theta_0} > y_i} (+1) $$\n", + "\n", + "3. Solve for $\\hat{\\theta_0}$.\n", + "$$ \n", + "0 = -\\frac{1}{n}\\sum_{\\hat{\\theta_0} < y_i} (1) + \\frac{1}{n}\\sum_{\\hat{\\theta_0} > y_i} (1) \\\\\n", + "\\sum_{\\hat{\\theta_0} < y_i} (1) = \\sum_{\\hat{\\theta_0} > y_i} (1) \n", + "$$\n", + "\n", + "Thus, the constant model parameter $\\theta = \\hat{\\theta_0}$ that minimizes MAE must satisfy\n", + "\n", + "$$ \\sum_{\\hat{\\theta_0} < y_i} (1) = \\sum_{\\hat{\\theta_0} > y_i} (1) $$\n", + "\n", + "In other words, the number of observations greater than $\\theta_0$ must be equal to the number of observations less than $\\theta_0$; there must be an equal number of points on the left and right side of the equation. This is the definition of median, so our optimal value is \n", + "$$ \\hat{\\theta_0} = median(y) $$ " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Summary: Loss Optimization, Calculus, and Critical Points\n", + "First, define the **objective function** as average loss \n", + "\n", + "* Plug in L1 or L2 loss.\n", + "* Plug in model so that resulting expression is a function of $\\theta$.\n", + "\n", + "Then, find the minimum of the objective function:\n", + "\n", + "1. Differentiate with respect to $\\theta$.\n", + "2. Set equal to 0.\n", + "3. Solve for $\\theta$.\n", + "4. (if we have multiple parameters) repeat the steps 1-3 with partial derivatives \n", + "\n", + "Recall critical points from calculus: $\\R(\\hat{\\theta})$ could be a minimum, maximum, or saddle point!\n", + "* We should technically also perform the second derivative test, i.e., show $\\R''(\\hat{\\theta}) > 0$\n", + "* MSE has a property—convexity—that guarantees that $\\R(\\hat{\\theta})$ is a global minimum.\n", + "* The proof of convexity for MAE is beyond this course.\n", + "\n", + "\n", + "\n", + "## Comparing Loss Functions\n", + "\n", + "Now, we've tried our hand at fitting a model under both MSE and MAE cost functions. How do the two results compare?\n", + "\n", + "Let's consider a dataset where each entry represents the number of drinks sold at a bubble tea store each day. We'll fit a constant model to predict the number of drinks that will be sold tomorrow." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#| code-fold: false\n", + "drinks = np.array([20, 21, 22, 29, 33])\n", + "drinks" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "From our derivations above, we know that the optimal model parameter under MSE cost is the mean of the dataset. Under MAE cost, the optimal parameter is the median of the dataset. " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#| code-fold: false\n", + "np.mean(drinks), np.median(drinks)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we plot each empirical risk function across several possible values of $\\theta$, we find that each $\\hat{\\theta}$ does indeed correspond to the lowest value of error:\n", + "\n", + "error\n", + "\n", + "Notice that the MSE above is a **smooth** function – it is differentiable at all points, making it easy to minimize using numerical methods. The MAE, in contrast, is not differentiable at each of its \"kinks.\" We'll explore how the smoothness of the cost function can impact our ability to apply numerical optimization in a few weeks. \n", + "\n", + "How do outliers affect each cost function? Imagine we replace the largest value in the dataset with 1000. The mean of the data increases substantially, while the median is nearly unaffected." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#| code-fold: false\n", + "drinks_with_outlier = np.append(drinks, 1000)\n", + "display(drinks_with_outlier)\n", + "np.mean(drinks_with_outlier), np.median(drinks_with_outlier)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This means that under the MSE, the optimal model parameter $\\hat{\\theta}$ is strongly affected by the presence of outliers. Under the MAE, the optimal parameter is not as influenced by outlying data. We can generalize this by saying that the MSE is **sensitive** to outliers, while the MAE is **robust** to outliers.\n", + "\n", + "Let's try another experiment. This time, we'll add an additional, non-outlying datapoint to the data." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#| code-fold: false\n", + "drinks_with_additional_observation = np.append(drinks, 35)\n", + "drinks_with_additional_observation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When we again visualize the cost functions, we find that the MAE now plots a horizontal line between 22 and 29. This means that there are *infinitely* many optimal values for the model parameter: any value $\\hat{\\theta} \\in [22, 29]$ will minimize the MAE. In contrast, the MSE still has a single best value for $\\hat{\\theta}$. In other words, the MSE has a **unique** solution for $\\hat{\\theta}$; the MAE is not guaranteed to have a single unique solution.\n", + "\n", + "compare_loss\n", + "\n", + "To summarize our example, \n", + "| -- | MSE (Mean Squared Loss) | MAE (Mean Absolute Loss) | \n", + "| -- | -- | -- | \n", + "| Loss Function | $R(\\theta) = \\frac{1}{n}\\sum^{n}_{i=1} (y_i - \\theta_0)^2 $ | $R(\\theta) = \\frac{1}{n}\\sum^{n}_{i=1} |y_i - \\theta_0 | $ |\n", + "| optimal $\\hat{\\theta_0}$ | $\\hat{\\theta_0} = mean(y) = \\bar{y} $ | $\\hat{\\theta_0} = median(y) $ |\n", + "| loss surface | ![](images/mse_loss.png) | 3-D ![](images/mae_loss.png) | \n", + "| | **Smooth** - easy to minimize using numerical methods | **Piecewise** - at each of the “kinks,” it’s not differentiable. Harder to minimize. | \n", + "| outliers | **Sensitive** to outliers (since they change mean substantially). Sensitivity also depends on the dataset size. | **More robust** to outliers. | \n", + "| $\\hat{\\theta_0}$ uniqueness | **unique** $\\hat{\\theta_0}$ | **Infinitely many** $\\hat{\\theta_0}$ | " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Transformations to fit Linear Models\n", + "\n", + "At this point, we have an effective method of fitting models to predict linear relationships. Given a feature variable and target, we can apply our four-step process to find the optimal model parameters. \n", + "\n", + "A key word above is *linear*. When we computed parameter estimates earlier, we assumed that $x_i$ and $y_i$ shared roughly a linear relationship. Data in the real world isn't always so straightforward, but we can transform the data to try and obtain linearity.\n", + "\n", + "The **Tukey-Mosteller Bulge Diagram** is a useful tool for summarizing what transformations can linearize the relationship between two variables. To determine what transformations might be appropriate, trace the shape of the \"bulge\" made by your data. Find the quadrant of the diagram that matches this bulge. The transformations shown on the vertical and horizontal axes of this quadrant can help improve the fit between the variables.\n", + "\n", + "bulge\n", + "\n", + "Note that: \n", + "* There are multiple solutions. Some will fit better than others. sqrt and log make a value “smaller”.\n", + "* Raising a value to a power makes it “bigger”.\n", + "* Each of these transformations equates to increasing or decreasing the scale of an axis.\n", + "\n", + "Other goals in addition to linearity are possible, for example making data appear more symmetric.\n", + "Linearity allows us to fit lines to the transformed data.\n", + "\n", + "Let's revisit our dugongs example. The lengths and ages and ages are plotted below: " + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#| code-fold: true\n", + "# `corrcoef` computes the correlation coefficient between two variables\n", + "# `std` finds the standard deviation\n", + "r = np.corrcoef(x, y)[0, 1]\n", + "theta_1 = r*np.std(y)/np.std(x)\n", + "theta_0 = np.mean(y) - theta_1*np.mean(x)\n", + "\n", + "fig, ax = plt.subplots(1, 2, dpi=200, figsize=(8, 3))\n", + "ax[0].scatter(x, y)\n", + "ax[0].set_xlabel(\"Length\")\n", + "ax[0].set_ylabel(\"Age\")\n", + "\n", + "ax[1].scatter(x, y)\n", + "ax[1].plot(x, theta_0 + theta_1*x, \"tab:red\")\n", + "ax[1].set_xlabel(\"Length\")\n", + "ax[1].set_ylabel(\"Age\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Looking at the plot on the left, we see that there is a slight curvature to the data points. Plotting the SLR curve on the right results in a poor fit.\n", + "\n", + "For SLR to perform well, we'd like there to be a rough linear trend relating `\"Age\"` and `\"Length\"`. What is making the raw data deviate from a linear relationship? Notice that the data points with `\"Length\"` greater than 2.6 have disproportionately high values of `\"Age\"` relative to the rest of the data. If we could manipulate these data points to have lower `\"Age\"` values, we'd \"shift\" these points downwards and reduce the curvature in the data. Applying a logarithmic transformation to $y_i$ (that is, taking $\\log($ `\"Age\"` $)$ ) would achieve just that.\n", + "\n", + "An important word on $\\log$: in Data 100 (and most upper-division STEM courses), $\\log$ denotes the natural logarithm with base $e$. The base-10 logarithm, where relevant, is indicated by $\\log_{10}$." + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#| code-fold: true\n", + "z = np.log(y)\n", + "\n", + "r = np.corrcoef(x, z)[0, 1]\n", + "theta_1 = r*np.std(z)/np.std(x)\n", + "theta_0 = np.mean(z) - theta_1*np.mean(x)\n", + "\n", + "fig, ax = plt.subplots(1, 2, dpi=200, figsize=(8, 3))\n", + "ax[0].scatter(x, z)\n", + "ax[0].set_xlabel(\"Length\")\n", + "ax[0].set_ylabel(r\"$\\log{(Age)}$\")\n", + "\n", + "ax[1].scatter(x, z)\n", + "ax[1].plot(x, theta_0 + theta_1*x, \"tab:red\")\n", + "ax[1].set_xlabel(\"Length\")\n", + "ax[1].set_ylabel(r\"$\\log{(Age)}$\")\n", + "\n", + "plt.subplots_adjust(wspace=0.3);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Our SLR fit looks a lot better! We now have a new target variable: the SLR model is now trying to predict the *log* of `\"Age\"`, rather than the untransformed `\"Age\"`. In other words, we are applying the transformation $z_i = \\log{(y_i)}$. The SLR model becomes:\n", + "\n", + "$$\\log{\\hat{(y_i)}} = \\theta_0 + \\theta_1 x_i$$\n", + "$$\\hat{z}_i = \\theta_0 + \\theta_1 x_i$$\n", + "\n", + "It turns out that this linearized relationship can help us understand the underlying relationship between $x_i$ and $y_i$. If we rearrange the relationship above, we find:\n", + "$$\n", + "\\log{(y_i)} = \\theta_0 + \\theta_1 x_i \\\\\n", + "y_i = e^{\\theta_0 + \\theta_1 x_i} \\\\\n", + "y_i = (e^{\\theta_0})e^{\\theta_1 x_i} \\\\\n", + "y_i = C e^{k x_i}\n", + "$$\n", + "\n", + "For some constants $C$ and $k$.\n", + "\n", + "$y_i$ is an *exponential* function of $x_i$. Applying an exponential fit to the untransformed variables corroborates this finding. " + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(dpi=120, figsize=(4, 3))\n", + "\n", + "plt.scatter(x, y)\n", + "plt.plot(x, np.exp(theta_0)*np.exp(theta_1*x), \"tab:red\")\n", + "plt.xlabel(\"Length\")\n", + "plt.ylabel(\"Age\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You may wonder: why did we choose to apply a log transformation specifically? Why not some other function to linearize the data?\n", + "\n", + "Practically, many other mathematical operations that modify the relative scales of `\"Age\"` and `\"Length\"` could have worked here.\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.9" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +}