lectures/CH-5-Causal-Model-Discovery.ipynb

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    "# Chapter 5: Causal Model Discovery from Data\n",
    "\n",
    "## Key Points Learned in this chapter\n",
    "\n",
    "### 1. Causal Discovery vs. Correlation  \n",
    "Causal discovery identifies cause-effect relationships, while correlation only measures statistical dependencies.\n",
    "\n",
    "### 2. PC Algorithm and Independence Testing  \n",
    "The PC algorithm discovers causal structures by testing conditional independence between variables.\n",
    "\n",
    "### 3. Score-Based Methods and GES  \n",
    "GES evaluates causal graphs by optimizing a score based on likelihood and graph complexity.\n",
    "\n",
    "### 4. Functional Causal Models: LiNGAM and ANM  \n",
    "LiNGAM and ANM assume specific functional forms, like linear and additive noise relationships.\n",
    "\n",
    "### 5. Evaluating Causal Models  \n",
    "Precision, recall, F1 score, and SHD assess how well discovered graphs match true relationships.\n",
    "\n",
    "### 5. Intervention and Countefactuals\n",
    "Show how to do intervention and countefactuals analysis using LiNGAM method.\n",
    "\n",
    "  \n",
    "---"
   ]
  },
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    "### 1. Introduction to Causal Model Discovery\n",
    "\n",
    "Causal model discovery identifies cause-effect relationships between variables using data. It is particularly useful in observational data where controlled experiments are impractical or impossible. Unlike correlation, which only measures statistical dependencies between variables, causal discovery seeks to uncover which variables influence others directly, enabling more accurate predictions and interventions.\n",
    "\n",
    "#### Healthcare Example: Causal Links Between Lifestyle and Health Outcomes\n",
    "In healthcare, causal discovery is used to understand how lifestyle factors (e.g., smoking, exercise) impact health outcomes such as heart disease and diabetes. Causal models help in identifying which factors to target for preventive measures.\n",
    "\n",
    "**Visualization: Correlation Matrix**\n"
   ]
  },
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   "outputs": [
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",
      "text/plain": [
       "<Figure size 500x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import networkx as nx\n",
    "\n",
    "# Hypothetical health dataset (replace with real data)\n",
    "df = pd.DataFrame({\n",
    "    'smoking': [5, 20, 15, 7, 10],\n",
    "    'exercise': [3, 2, 5, 6, 4],\n",
    "    'heart_disease': [1, 1, 0, 0, 1]\n",
    "})\n",
    "\n",
    "# Visualize correlations between variables\n",
    "plt.figure(figsize=(5, 4))\n",
    "sns.heatmap(df.corr(), annot=True, cmap='coolwarm')\n",
    "plt.title('Correlation Matrix of Health Variables')\n",
    "plt.show()\n",
    "\n",
    "# Create a Directed Acyclic Graph (DAG) representing causal assumptions\n",
    "G = nx.DiGraph()\n",
    "\n",
    "# Add edges according to causal assumptions\n",
    "G.add_edge('smoking', 'heart_disease')\n",
    "G.add_edge('exercise', 'heart_disease')\n",
    "\n",
    "# Visualize the DAG\n",
    "plt.figure(figsize=(5, 4))\n",
    "pos = nx.spring_layout(G)\n",
    "nx.draw(G, pos, with_labels=True, node_color='lightblue', node_size=2000, font_size=12, font_weight='bold', arrows=True)\n",
    "plt.title(\"Causal DAG: Smoking and Exercise Influence Heart Disease\")\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "48314992-3c99-4289-9fe1-0d8eecf60aa8",
   "metadata": {},
   "source": [
    "In this example, we plot a correlation matrix to observe the relationships between three variables: smoking, exercise, and heart disease. The correlation matrix shows how strongly each pair of variables is related to each other, but it does not imply causality. For example, smoking might have a strong correlation with heart disease, but to truly understand the causal relationship, we need more advanced methods like those in this chapter.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c168e7eb-b0c1-4ce2-8c12-62ce8b488ecd",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 2. Methods of Causal Discovery\n",
    "\n",
    "Causal discovery methods aim to infer causal relationships from observational data. These methods can be broadly categorized into three main groups, each with its own strengths and assumptions. We'll explore these categories and delve deeper into the PC Algorithm as an example of independence-based methods.\n",
    "\n",
    "\n",
    "### 2.1 Overview of Causal Discovery Methods\n",
    "\n",
    "1. **Independence-based methods**\n",
    "   - Rely on conditional independence tests\n",
    "   - Examples: PC Algorithm, FCI (Fast Causal Inference)\n",
    "   - Strengths: Can handle high-dimensional data, robust to some forms of model misspecification\n",
    "   - Limitations: Sensitive to errors in independence tests, assume causal sufficiency (no unmeasured confounders)\n",
    "\n",
    "2. **Score-based methods**\n",
    "   - Use a scoring function to evaluate and compare different causal structures\n",
    "   - Examples: Greedy Equivalence Search (GES), Bayesian network learning algorithms\n",
    "   - Strengths: Can incorporate prior knowledge, often more robust to small sample sizes\n",
    "   - Limitations: Can be computationally intensive for large networks\n",
    "\n",
    "3. **Functional causal discovery methods**\n",
    "   - Exploit additional assumptions about the functional form of causal relationships\n",
    "   - Examples: LiNGAM (Linear Non-Gaussian Acyclic Model), ANM (Additive Noise Model)\n",
    "   - Strengths: Can identify causal direction in certain cases where other methods fail\n",
    "   - Limitations: Rely on specific assumptions about functional forms and noise distributions\n",
    "\n",
    "---\n",
    "\n",
    "### 2.2 Independence-Based Methods: The PC Algorithm\n",
    "\n",
    "The PC Algorithm, named after its inventors Peter Spirtes and Clark Glymour, is a fundamental algorithm in the field of causal discovery. It belongs to the class of constraint-based methods, which rely on conditional independence tests to infer causal structures ([refrence](https://applied-informatics-j.springeropen.com/articles/10.1186/s40535-016-0018-x)).\n",
    "\n",
    "#### Key Concepts\n",
    "\n",
    "1. **Causal Markov Assumption**: Given a causal DAG (Directed Acyclic Graph), each variable is independent of its non-descendants given its parents.\n",
    "\n",
    "2. **Faithfulness Assumption**: All conditional independence relationships in the data are implied by the causal Markov assumption applied to the true causal graph.\n",
    "\n",
    "#### Mathematical Formulation\n",
    "\n",
    "The PC Algorithm aims to identify conditional independence relationships of the form:\n",
    "\n",
    "$$\n",
    "X_i \\perp X_j \\mid \\mathbf{S}\n",
    "$$\n",
    "\n",
    "where $X_i$ and $X_j$ are variables in the dataset, and $\\mathbf{S}$ is a subset of the other variables. The symbol $\\perp$ denotes statistical independence.\n",
    "\n",
    "#### Algorithm Steps\n",
    "\n",
    "1. **Start with a complete undirected graph**\n",
    "   - Initially assume all variables are connected\n",
    "\n",
    "2. **Edge removal phase**\n",
    "   - For each pair of variables $(X_i, X_j)$:\n",
    "     - Test for marginal independence: $X_i \\perp X_j$\n",
    "     - If independent, remove the edge between $X_i$ and $X_j$\n",
    "   - For increasing conditioning set sizes:\n",
    "     - Test conditional independence: $X_i \\perp X_j \\mid \\mathbf{S}$\n",
    "     - If a separating set $\\mathbf{S}$ is found, remove the edge\n",
    "\n",
    "3. **Edge orientation phase**\n",
    "   - Orient v-structures: $X_i \\rightarrow X_k \\leftarrow X_j$ if $X_i$ and $X_j$ are not adjacent and $X_k$ is not in the separating set of $X_i$ and $X_j$\n",
    "   - Apply orientation rules to derive additional edge directions\n",
    "\n",
    "#### Mathematical Details of Independence Testing\n",
    "\n",
    "For Gaussian variables, conditional independence can be tested using partial correlations:\n",
    "\n",
    "$$\n",
    "\\rho_{X_i,X_j|\\mathbf{S}} = \\frac{\\rho_{X_i,X_j} - \\rho_{X_i,\\mathbf{S}}\\rho_{X_j,\\mathbf{S}}}{\\sqrt{(1-\\rho_{X_i,\\mathbf{S}}^2)(1-\\rho_{X_j,\\mathbf{S}}^2)}}\n",
    "$$\n",
    "\n",
    "Where $\\rho_{X_i,X_j|\\mathbf{S}}$ is the partial correlation between $X_i$ and $X_j$ given $\\mathbf{S}$.\n",
    "\n",
    "For discrete variables, conditional independence can be tested using the G-test or chi-squared test.\n",
    "\n",
    "\n",
    "#### Example: Disease-Symptom Causal Discovery\n",
    "We use the PC algorithm to learn the causal relationships between diseases (e.g., tuberculosis, bronchitis) and symptoms (e.g., dyspnea).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "ef55c866-d063-47d1-b99c-0ab3d09848f9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "9576912151db42c3b82afdc8c32558fc",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/5 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "from pgmpy.estimators import PC\n",
    "from pgmpy.independencies import Independencies\n",
    "\n",
    "# Generate synthetic data\n",
    "np.random.seed(42)\n",
    "n_samples = 1000\n",
    "\n",
    "# Simulate causal relationships\n",
    "tuberculosis = np.random.binomial(1, 0.05, n_samples)\n",
    "smoking = np.random.binomial(1, 0.2, n_samples)\n",
    "lung_cancer = np.random.binomial(1, 0.01 + 0.1*tuberculosis + 0.3*smoking, n_samples)\n",
    "cough = np.random.binomial(1, 0.1 + 0.6*tuberculosis + 0.3*lung_cancer, n_samples)\n",
    "\n",
    "data = pd.DataFrame({\n",
    "    'Tuberculosis': tuberculosis,\n",
    "    'Smoking': smoking,\n",
    "    'Lung Cancer': lung_cancer,\n",
    "    'Cough': cough\n",
    "})\n",
    "\n",
    "# Apply PC algorithm\n",
    "pc = PC(data)\n",
    "estimated_model = pc.estimate()\n",
    "\n",
    "# Visualize the result with a smaller DAG\n",
    "G = nx.DiGraph()\n",
    "G.add_edges_from(estimated_model.edges())\n",
    "\n",
    "# Adjust the figure size to make the DAG smaller\n",
    "pos = nx.spring_layout(G)\n",
    "plt.figure(figsize=(5, 4))  # Smaller figure size\n",
    "nx.draw(G, pos, with_labels=True, node_color='lightblue', node_size=1500, font_size=10, font_weight='bold')\n",
    "nx.draw_networkx_edge_labels(G, pos, edge_labels={(u, v): '' for (u, v) in G.edges()})\n",
    "plt.title(\"Estimated Causal Graph using PC Algorithm\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "005c4cd9-7adb-42fb-aaea-9ffd9889466d",
   "metadata": {},
   "source": [
    "After applying the PC algorithm, a causal graph is generated showing the relationships between diseases (e.g., tuberculosis, bronchitis) and symptoms (e.g., dyspnea). "
   ]
  },
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    "---\n",
    "\n",
    "## 2.2 Score-Based Methods: Greedy Equivalence Search (GES)\n",
    "\n",
    "Score-based methods in causal discovery aim to find the causal graph that best explains the observed data according to a predefined scoring criterion. Among these methods, Greedy Equivalence Search (GES) stands out as a popular and efficient algorithm ([Reference](https://www.jmlr.org/papers/volume3/chickering02b/chickering02b.pdf)).\n",
    "\n",
    "### Overview of Greedy Equivalence Search (GES)\n",
    "\n",
    "Greedy Equivalence Search, introduced by Chickering (2002), is a search-based algorithm that explores the space of possible causal graphs to find the one that maximizes a given score function. GES operates on equivalence classes of Directed Acyclic Graphs (DAGs), known as Completed Partially Directed Acyclic Graphs (CPDAGs).\n",
    "\n",
    "Key features of GES:\n",
    "1. Starts with an empty graph and performs a forward phase of edge additions\n",
    "2. Follows with a backward phase of edge removals\n",
    "3. Uses a scoring criterion to evaluate graph changes\n",
    "4. Guarantees to find the optimal graph under certain assumptions\n",
    "\n",
    "### Mathematical Formulation\n",
    "\n",
    "GES typically uses the Bayesian Information Criterion (BIC) as its scoring function, though other scores like the Akaike Information Criterion (AIC) or Minimum Description Length (MDL) can also be used ([Reference](https://www.jmlr.org/papers/volume5/chickering04a/chickering04a.pdf)).\n",
    "\n",
    "#### Bayesian Information Criterion (BIC)\n",
    "\n",
    "The BIC score for a model $M$ is defined as:\n",
    "\n",
    "$$\n",
    "\\text{BIC}(M) = \\log \\mathcal{L}(M \\mid D) - \\frac{k \\log N}{2}\n",
    "$$\n",
    "\n",
    "Where:\n",
    "- $\\mathcal{L}(M \\mid D)$ is the likelihood of the model given data $D$\n",
    "- $k$ is the number of free parameters in the model\n",
    "- $N$ is the number of observations in the dataset\n",
    "\n",
    "The BIC balances model fit (captured by the likelihood term) with model complexity (penalized by the second term).\n",
    "\n",
    "#### GES Algorithm Steps\n",
    "\n",
    "1. **Forward Phase**: \n",
    "   Start with an empty graph and iteratively add edges that maximize the increase in the BIC score.\n",
    "   \n",
    "   For each potential edge addition $e$:\n",
    "   $$\\Delta \\text{BIC}(e) = \\text{BIC}(M_{new}) - \\text{BIC}(M_{current})$$\n",
    "   Add the edge $e$ that maximizes $\\Delta \\text{BIC}(e)$ if it's positive.\n",
    "\n",
    "2. **Backward Phase**: \n",
    "   Starting from the graph obtained in the forward phase, iteratively remove edges that maximize the increase in the BIC score.\n",
    "   \n",
    "   For each potential edge removal $e$:\n",
    "   $$\\Delta \\text{BIC}(e) = \\text{BIC}(M_{new}) - \\text{BIC}(M_{current})$$\n",
    "   Remove the edge $e$ that maximizes $\\Delta \\text{BIC}(e)$ if it's positive.\n",
    "\n",
    "3. **Stopping Criterion**: \n",
    "   The algorithm stops when no edge addition or removal can increase the BIC score.\n",
    "\n",
    "### Theoretical Guarantees\n",
    "\n",
    "Under certain assumptions, including:\n",
    "- The true causal structure is a DAG\n",
    "- The data is generated from a multivariate Gaussian distribution\n",
    "- The sample size is sufficiently large\n",
    "\n",
    "GES is guaranteed to recover the correct Markov equivalence class of the true causal graph.\n",
    "\n",
    "### Advantages and Limitations\n",
    "\n",
    "Advantages:\n",
    "1. Can handle high-dimensional data efficiently\n",
    "2. Provides a principled way to balance model fit and complexity\n",
    "3. Has theoretical guarantees under certain conditions\n",
    "\n",
    "Limitations:\n",
    "1. Assumes causal sufficiency (no unmeasured confounders)\n",
    "2. May struggle with non-linear relationships or non-Gaussian noise\n",
    "3. Can be sensitive to hyperparameter choices and sample size\n",
    "\n",
    "\n",
    "#### Example: Economic Factors Causal Discovery\n",
    "We use GES to identify causal relationships between macroeconomic variables such as inflation, interest rates, and unemployment.\n"
   ]
  },
  {
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   "execution_count": 101,
   "id": "6e3751c3-0e61-4237-a42f-fd489c688736",
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",
      "text/plain": [
       "<Figure size 500x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "from pgmpy.estimators import ExhaustiveSearch\n",
    "\n",
    "# Generate synthetic economic data\n",
    "np.random.seed(42)\n",
    "n_samples = 1000\n",
    "\n",
    "gdp = np.random.normal(0, 1, n_samples)\n",
    "unemployment = -0.5 * gdp + np.random.normal(0, 0.5, n_samples)\n",
    "inflation = 0.3 * gdp - 0.2 * unemployment + np.random.normal(0, 0.5, n_samples)\n",
    "interest_rate = 0.4 * inflation + np.random.normal(0, 0.3, n_samples)\n",
    "\n",
    "data = pd.DataFrame({\n",
    "    'GDP': gdp,\n",
    "    'Unemployment': unemployment,\n",
    "    'Inflation': inflation,\n",
    "    'Interest Rate': interest_rate\n",
    "})\n",
    "\n",
    "# Apply GES (using ExhaustiveSearch as a substitute)\n",
    "es = ExhaustiveSearch(data)\n",
    "best_model = es.estimate()\n",
    "\n",
    "# Visualize the result with a smaller DAG\n",
    "G = nx.DiGraph()\n",
    "G.add_edges_from(best_model.edges())\n",
    "\n",
    "# Adjust the figure size, node size, and font size for a smaller DAG\n",
    "pos = nx.spring_layout(G)\n",
    "plt.figure(figsize=(5, 4))  # Reduced figure size\n",
    "nx.draw(G, pos, with_labels=True, node_color='lightgreen', node_size=1500, font_size=10, font_weight='bold')\n",
    "nx.draw_networkx_edge_labels(G, pos, edge_labels={(u, v): '' for (u, v) in G.edges()})\n",
    "plt.title(\"Estimated Causal Graph using GES Algorithm\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d8abafe-29d2-4343-abd4-0b2f7223c44d",
   "metadata": {},
   "source": [
    "The GES algorithm estimates a causal graph between macroeconomic variables such as inflation, interest rates, and unemployment. The estimated graph shows which factors influence others. For instance, the graph might show that inflation causally affects interest rates. The precision of this estimation is influenced by the scoring criterion (such as BIC) used in GES."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08b45d6d-a646-4de4-9812-6ba000cf1f6a",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 2.3 Functional Causal Discovery: LiNGAM and Additive Noise Models (ANM)\n",
    "\n",
    "Functional causal discovery methods aim to infer causal relationships from observational data by leveraging specific assumptions about the functional form of causal mechanisms and the properties of noise terms. Two prominent approaches in this category are Linear Non-Gaussian Acyclic Models (LiNGAM) and Additive Noise Models (ANM).\n",
    "\n",
    "### LiNGAM (Linear Non-Gaussian Acyclic Model)\n",
    "\n",
    "LiNGAM is a framework for causal discovery that combines linear relationships with non-Gaussian noise assumptions. It was introduced by Shimizu et al. (2006) as a method to overcome limitations of traditional causal discovery algorithms that rely on Gaussian assumptions ([Reference](https://www.jmlr.org/papers/volume7/shimizu06a/shimizu06a.pdf)).\n",
    "\n",
    "Key features of LiNGAM:\n",
    "- Assumes linear relationships between variables\n",
    "- Requires non-Gaussian noise for identifiability\n",
    "- Can identify the full causal structure, including causal ordering and effect sizes\n",
    "\n",
    "#### Mathematical Formulation of LiNGAM:\n",
    "\n",
    "LiNGAM assumes that each variable $X_i$ can be written as a linear function of its parents:\n",
    "\n",
    "$X_i = \\sum_{j \\in \\text{PA}(i)} a_{ij}X_j + e_i$\n",
    "\n",
    "Where:\n",
    "- $X_i$ is the i-th observed variable\n",
    "- $\\text{PA}(i)$ is the set of parent variables of $X_i$ in the causal graph\n",
    "- $a_{ij}$ are the linear coefficients (causal effects)\n",
    "- $e_i$ is the noise term, assumed to be non-Gaussian and independent of each other\n",
    "\n",
    "The non-Gaussian nature of $e_i$ is crucial for the identifiability of the model. LiNGAM leverages Independent Component Analysis (ICA) to estimate the causal structure from the observed data.\n",
    "\n",
    "### Additive Noise Models (ANM)\n",
    "\n",
    "Additive Noise Models, introduced by Hoyer et al. (2009), extend the idea of functional causal discovery to nonlinear relationships while maintaining the additive noise assumption ([Reference](https://proceedings.neurips.cc/paper/2008/file/f7664060cc52bc6f3d620bcedc94a4b6-Paper.pdf)).\n",
    "\n",
    "Key features of ANM:\n",
    "- Allows for nonlinear relationships between cause and effect\n",
    "- Assumes additive and independent noise in the causal direction\n",
    "- Can identify causal direction in two-variable systems and, under certain conditions, in multivariate systems\n",
    "\n",
    "#### Mathematical Formulation of ANM:\n",
    "\n",
    "For a simple bivariate case where $X$ causes $Y$, the ANM assumes:\n",
    "\n",
    "$Y = f(X) + \\epsilon_Y \\quad \\text{with} \\quad \\epsilon_Y \\perp X$\n",
    "\n",
    "Where:\n",
    "- $f(X)$ is a (possibly nonlinear) function of $X$\n",
    "- $\\epsilon_Y$ is the noise term, assumed to be independent of $X$\n",
    "- $\\perp$ denotes statistical independence\n",
    "\n",
    "The key insight of ANM is that this independence between $X$ and $\\epsilon_Y$ typically holds only in the true causal direction. In the reverse direction, the noise term would generally not be independent of the supposed cause.\n",
    "\n",
    "### Comparison and Applications\n",
    "\n",
    "Both LiNGAM and ANM offer powerful tools for causal discovery, each with its strengths:\n",
    "\n",
    "1. **Linearity vs. Nonlinearity**: LiNGAM is restricted to linear relationships but can handle multivariate systems more easily. ANM allows for nonlinear relationships but is most straightforward in bivariate cases.\n",
    "\n",
    "2. **Noise Assumptions**: LiNGAM requires non-Gaussian noise, while ANM focuses on the independence of noise from the cause.\n",
    "\n",
    "3. **Identifiability**: LiNGAM can identify the full causal structure in multivariate systems. ANM provides strong identifiability results for bivariate systems and certain classes of multivariate systems.\n",
    "\n",
    "4. **Computational Complexity**: LiNGAM often has lower computational complexity, especially for large systems, due to its linear nature.\n",
    "\n",
    "   \n",
    "#### Example: Gene Expression Causal Discovery\n",
    "We apply LiNGAM to discover causal relationships between gene expressions and disease outcomes.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "2ba29c20-113f-431d-9650-6a777f4b62a3",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 500x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.preprocessing import scale\n",
    "from lingam import DirectLiNGAM\n",
    "\n",
    "# Generate synthetic gene expression data\n",
    "np.random.seed(42)\n",
    "n_samples = 1000\n",
    "\n",
    "gene1 = np.random.normal(0, 1, n_samples)\n",
    "gene2 = 0.5 * gene1 + np.random.normal(0, 0.5, n_samples)\n",
    "gene3 = -0.3 * gene1 + 0.4 * gene2 + np.random.normal(0, 0.5, n_samples)\n",
    "phenotype = 0.6 * gene2 - 0.4 * gene3 + np.random.normal(0, 0.3, n_samples)\n",
    "\n",
    "data = pd.DataFrame({\n",
    "    'Gene1': gene1,\n",
    "    'Gene2': gene2,\n",
    "    'Gene3': gene3,\n",
    "    'Phenotype': phenotype\n",
    "})\n",
    "\n",
    "# Scale the data\n",
    "scaled_data = scale(data)\n",
    "\n",
    "# Apply LiNGAM\n",
    "model = DirectLiNGAM()\n",
    "model.fit(scaled_data)\n",
    "\n",
    "# Visualize the result with a smaller DAG\n",
    "G = nx.DiGraph()\n",
    "for i, j in zip(*np.where(model.adjacency_matrix_ != 0)):\n",
    "    G.add_edge(data.columns[i], data.columns[j])\n",
    "\n",
    "# Adjust the figure size, node size, and font size for a smaller DAG\n",
    "pos = nx.spring_layout(G)\n",
    "plt.figure(figsize=(5, 4))  # Reduced figure size\n",
    "nx.draw(G, pos, with_labels=True, node_color='lightcoral', node_size=1500, font_size=10, font_weight='bold')\n",
    "nx.draw_networkx_edge_labels(G, pos, edge_labels={(u, v): f'{model.adjacency_matrix_[list(G.nodes()).index(u), list(G.nodes()).index(v)]:.2f}' for (u, v) in G.edges()})\n",
    "plt.title(\"Estimated Causal Graph using LiNGAM Algorithm\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6622f8ca-0c27-4210-a5f7-6f5945a1e38e",
   "metadata": {},
   "source": [
    "The LiNGAM algorithm estimates a causal graph showing relationships between gene expressions and a phenotype (disease outcome). Each edge in the graph is weighted, indicating the strength of the causal relationship between genes and the disease. For example, the result may show that gene 1 causally affects gene 2, and gene 2 in turn affects the disease. The weights on the edges provide insights into how strongly these genes influence each other and the disease."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb2f6fd5-e632-4543-888d-f14971871fee",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 3. Advanced Gradient-Based Methods: NOTEARS\n",
    "\n",
    "NOTEARS (Non-combinatorial Optimization via Trace Exponential and Augmented lagRangian for Structure learning) is a novel approach to causal discovery that reformulates the problem as a continuous optimization task. This method, introduced by Zheng et al. (2018), represents a significant departure from traditional constraint-based and score-based methods ([Reference](https://proceedings.neurips.cc/paper/2018/file/e347c51419ffb23ca3fd5050202f9c3d-Paper.pdf)).\n",
    "\n",
    "### Key Concepts\n",
    "\n",
    "1. **Continuous Optimization**: NOTEARS transforms the discrete problem of graph structure learning into a continuous optimization problem.\n",
    "2. **Acyclicity Constraint**: It introduces a differentiable constraint to ensure the learned graph is acyclic.\n",
    "3. **Gradient-Based Learning**: The method leverages efficient gradient-based optimization techniques.\n",
    "\n",
    "### Mathematical Formulation\n",
    "\n",
    "Given a dataset $X \\in \\mathbb{R}^{n \\times d}$ where $n$ is the number of samples and $d$ is the number of variables, NOTEARS aims to learn a weighted adjacency matrix $W \\in \\mathbb{R}^{d \\times d}$ representing the causal graph.\n",
    "\n",
    "#### Objective Function\n",
    "\n",
    "The primary optimization objective is:\n",
    "\n",
    "$$\n",
    "\\min_W \\frac{1}{2n} \\|X - XW\\|_F^2 + \\lambda \\|W\\|_1\n",
    "$$\n",
    "\n",
    "Where:\n",
    "- $\\|X - XW\\|_F^2$ is the squared Frobenius norm of the prediction error (assuming a linear structural equation model)\n",
    "- $\\|W\\|_1$ is the L1 norm of $W$, promoting sparsity\n",
    "- $\\lambda$ is a regularization parameter controlling the trade-off between fit and sparsity\n",
    "\n",
    "#### Acyclicity Constraint\n",
    "\n",
    "The key innovation of NOTEARS is the acyclicity constraint:\n",
    "\n",
    "$$\n",
    "h(W) = \\text{tr}(e^{W \\circ W}) - d = 0\n",
    "$$\n",
    "\n",
    "Where:\n",
    "- $\\text{tr}(\\cdot)$ is the trace operator\n",
    "- $e^{(\\cdot)}$ is the matrix exponential\n",
    "- $\\circ$ denotes the Hadamard (element-wise) product\n",
    "- $d$ is the number of variables\n",
    "\n",
    "This constraint ensures that the resulting graph is acyclic. Intuitively, $\\text{tr}(e^{W \\circ W})$ counts the number of cycles of all lengths in the graph.\n",
    "\n",
    "### Algorithm Steps\n",
    "\n",
    "1. **Initialization**: Start with a random or zero initialization of $W$.\n",
    "\n",
    "2. **Augmented Lagrangian Optimization**:\n",
    "   - Define the augmented Lagrangian:\n",
    "     $$\\mathcal{L}(W, \\lambda, \\rho) = f(W) + \\lambda h(W) + \\frac{\\rho}{2} h(W)^2$$\n",
    "     \n",
    "   - Alternately optimize $W$ and update $\\lambda, \\rho$ until convergence:\n",
    "     \n",
    "     a. $W^{(t+1)} = \\arg\\min_W \\mathcal{L}(W, \\lambda^{(t)}, \\rho^{(t)})$ \\\n",
    "     b. $\\lambda^{(t+1)} = \\lambda^{(t)} + \\rho^{(t)} h(W^{(t+1)})$ \\\n",
    "     c. $\\rho^{(t+1)} = \\min(\\gamma \\rho^{(t)}, \\rho_{\\max})$\n",
    "\n",
    "3. **Thresholding**: Apply a threshold to $W$ to obtain the final DAG structure.\n",
    "\n",
    "\n",
    "#### Example: Social Network User Behavior\n",
    "We apply NOTEARS to discover causal relationships in social network data.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "5f42741c-cef2-4223-ab94-57feb335fc9d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Correlation Matrix:\n",
      "                    Posts     Likes    Shares  User Engagement\n",
      "Posts            1.000000  0.700310  0.656480         0.667229\n",
      "Likes            0.700310  1.000000  0.710076         0.808642\n",
      "Shares           0.656480  0.710076  1.000000         0.849897\n",
      "User Engagement  0.667229  0.808642  0.849897         1.000000\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.covariance import GraphicalLassoCV\n",
    "\n",
    "# Generate synthetic social network data\n",
    "np.random.seed(42)\n",
    "n_samples = 1000\n",
    "posts = np.random.poisson(5, n_samples)\n",
    "likes = 0.7 * posts + np.random.poisson(3, n_samples)\n",
    "shares = 0.3 * posts + 0.5 * likes + np.random.poisson(2, n_samples)\n",
    "user_engagement = 0.4 * likes + 0.6 * shares + np.random.normal(0, 1, n_samples)\n",
    "\n",
    "data = pd.DataFrame({\n",
    "    'Posts': posts,\n",
    "    'Likes': likes,\n",
    "    'Shares': shares,\n",
    "    'User Engagement': user_engagement\n",
    "})\n",
    "\n",
    "# Standardize the data\n",
    "scaler = StandardScaler()\n",
    "scaled_data = scaler.fit_transform(data)\n",
    "\n",
    "# Estimate the graphical structure using Graphical Lasso\n",
    "model = GraphicalLassoCV()\n",
    "model.fit(scaled_data)\n",
    "\n",
    "# Get the precision matrix (inverse covariance)\n",
    "precision_matrix = model.precision_\n",
    "\n",
    "# Create a graph from the precision matrix\n",
    "G = nx.Graph()\n",
    "for i in range(precision_matrix.shape[0]):\n",
    "    for j in range(i+1, precision_matrix.shape[1]):\n",
    "        if abs(precision_matrix[i, j]) > 1e-3:  # Threshold to consider an edge\n",
    "            G.add_edge(data.columns[i], data.columns[j], weight=abs(precision_matrix[i, j]))\n",
    "\n",
    "# Visualize the result with a smaller DAG\n",
    "pos = nx.spring_layout(G)\n",
    "plt.figure(figsize=(5, 4))  # Reduced figure size\n",
    "nx.draw(G, pos, with_labels=True, node_color='lightyellow', node_size=1500, font_size=10, font_weight='bold')\n",
    "edge_labels = nx.get_edge_attributes(G, 'weight')\n",
    "nx.draw_networkx_edge_labels(G, pos, edge_labels={e: f'{w:.2f}' for e, w in edge_labels.items()})\n",
    "plt.title(\"Estimated Relationship Graph using Graphical Lasso\")\n",
    "plt.show()\n",
    "\n",
    "# Print correlation matrix\n",
    "print(\"Correlation Matrix:\")\n",
    "print(data.corr())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f4c9472a-4df4-4b48-811e-c9abed2b1dfe",
   "metadata": {},
   "source": [
    " In this example, we apply the NOTEARS algorithm to synthetic social network data, such as posts, likes, and user engagement. The resulting causal graph shows which behaviors influence others. For example, the graph may show that posts causally influence likes, and likes, in turn, influence shares. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72d7bad1-9451-425e-a204-ca961f0c21b5",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 4. Hybrid Approaches and Integration with Expert Knowledge\n",
    "\n",
    "In complex real-world scenarios, purely data-driven methods for causal discovery may fall short of providing accurate and meaningful results. This limitation arises from various factors such as the presence of hidden confounders, complex non-linear relationships, or insufficient data. To address these challenges, researchers have developed hybrid approaches that combine machine learning algorithms with domain expertise. These methods aim to leverage the strengths of both computational techniques and human knowledge to improve the accuracy and interpretability of discovered causal structures ([Reference](https://www.annualreviews.org/doi/full/10.1146/annurev-statistics-031017-100630)).\n",
    "\n",
    "### 4.1 Motivation for Hybrid Approaches\n",
    "\n",
    "1. **Limitations of Pure Data-Driven Methods**:\n",
    "   - Inability to detect certain causal relationships due to faithfulness violations\n",
    "   - Difficulty in handling latent confounders\n",
    "   - Challenges in distinguishing between causal and merely correlational relationships\n",
    "   - Potential for discovering spurious causal links in high-dimensional settings\n",
    "\n",
    "2. **Advantages of Expert Knowledge**:\n",
    "   - Incorporation of domain-specific constraints and known causal relationships\n",
    "   - Ability to guide the search process and reduce the space of possible causal structures\n",
    "   - Improved interpretability and practical relevance of the discovered causal graphs\n",
    "   - Potential to overcome limitations of data-driven methods in specific scenarios\n",
    "\n",
    "### 4.2 Types of Expert Knowledge Integration\n",
    "\n",
    "1. **Prior Knowledge on Causal Relationships**:\n",
    "   - Specifying known direct causal links\n",
    "   - Excluding impossible causal relationships\n",
    "   - Defining temporal ordering of variables\n",
    "\n",
    "2. **Structural Constraints**:\n",
    "   - Enforcing specific graph structures (e.g., hierarchical relationships)\n",
    "   - Limiting the maximum number of parents for each node\n",
    "\n",
    "3. **Parameter Constraints**:\n",
    "   - Specifying ranges or distributions for causal effect sizes\n",
    "   - Imposing monotonicity constraints on causal relationships\n",
    "\n",
    "4. **Contextual Information**:\n",
    "   - Incorporating knowledge about data collection processes\n",
    "   - Accounting for known interventions or experimental designs\n",
    "\n",
    "  \n",
    "#### Example: Climate Change Causal Analysis\n",
    "We combine observational data with expert knowledge to refine causal discovery results in climate change research.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "1164177c-08fb-4828-b261-a6e6ba646f41",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f35190d35bdc4a4797e844e723b122ec",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/5 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "from pgmpy.estimators import PC\n",
    "from pgmpy.models import BayesianNetwork\n",
    "\n",
    "# Generate synthetic climate data\n",
    "np.random.seed(42)\n",
    "n_samples = 1000\n",
    "\n",
    "co2_emissions = np.random.normal(400, 30, n_samples)\n",
    "temperature = 0.5 * co2_emissions + np.random.normal(15, 1, n_samples)\n",
    "sea_level = 0.3 * temperature + np.random.normal(0, 0.1, n_samples)\n",
    "arctic_ice = -0.4 * temperature + np.random.normal(10, 1, n_samples)\n",
    "\n",
    "data = pd.DataFrame({\n",
    "    'CO2 Emissions': co2_emissions,\n",
    "    'Temperature': temperature,\n",
    "    'Sea Level': sea_level,\n",
    "    'Arctic Ice': arctic_ice\n",
    "})\n",
    "\n",
    "# Apply PC algorithm\n",
    "pc = PC(data)\n",
    "estimated_model = pc.estimate()\n",
    "\n",
    "# Expert knowledge: CO2 emissions affect temperature\n",
    "expert_edges = [('CO2 Emissions', 'Temperature')]\n",
    "\n",
    "# Integrate expert knowledge\n",
    "final_model = BayesianNetwork()\n",
    "final_model.add_edges_from(estimated_model.edges())\n",
    "final_model.add_edges_from(expert_edges)\n",
    "\n",
    "# Visualize the result with a smaller DAG\n",
    "G = nx.DiGraph()\n",
    "G.add_edges_from(final_model.edges())\n",
    "\n",
    "# Adjust the figure size, node size, and font size to make the DAG smaller\n",
    "pos = nx.spring_layout(G)\n",
    "plt.figure(figsize=(5, 4))  # Reduced figure size\n",
    "nx.draw(G, pos, with_labels=True, node_color='lightblue', node_size=1500, font_size=10, font_weight='bold')\n",
    "nx.draw_networkx_edge_labels(G, pos, edge_labels={(u, v): 'Expert' if (u, v) in expert_edges else 'Data' for (u, v) in G.edges()})\n",
    "plt.title(\"Hybrid Causal Graph: Climate Change Factors\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "962b7201-3010-423f-8db6-b36fdc16b00d",
   "metadata": {},
   "source": [
    "The hybrid approach integrates data-driven causal discovery methods with expert knowledge. The resulting causal graph shows how CO2 emissions causally influence global warming-related variables. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a76c25f-48b8-461a-ba1f-5a2dd9959124",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 5. Evaluating Causal Discovery Models\n",
    "\n",
    "Evaluating the performance of causal discovery algorithms is crucial for assessing their reliability and comparing different methods. Unlike traditional machine learning tasks, evaluating causal discovery models presents unique challenges due to the structural nature of the output and the potential for equivalent causal structures. This section explores various metrics and approaches used to evaluate causal discovery models ([Reference](https://www.frontiersin.org/journals/genetics/articles/10.3389/fgene.2019.00524/full)).\n",
    "\n",
    "### 5.1 Evaluation Metrics\n",
    "\n",
    "#### Precision\n",
    "\n",
    "Precision measures the proportion of correctly identified causal relationships among all relationships identified by the model.\n",
    "\n",
    "$$\n",
    "\\text{Precision} = \\frac{\\text{True Positives}}{\\text{True Positives} + \\text{False Positives}}\n",
    "$$\n",
    "\n",
    "#### Recall\n",
    "\n",
    "Recall measures the proportion of correctly identified causal relationships among all true causal relationships in the ground truth.\n",
    "\n",
    "$$\n",
    "\\text{Recall} = \\frac{\\text{True Positives}}{\\text{True Positives} + \\text{False Negatives}}\n",
    "$$\n",
    "\n",
    "#### F1 Score\n",
    "\n",
    "The F1 score is the harmonic mean of precision and recall, providing a balanced measure of the model's performance.\n",
    "\n",
    "$$\n",
    "\\text{F1 Score} = 2 \\cdot \\frac{\\text{Precision} \\cdot \\text{Recall}}{\\text{Precision} + \\text{Recall}}\n",
    "$$\n",
    "\n",
    "#### Structural Hamming Distance (SHD)\n",
    "\n",
    "SHD measures the number of edge additions, deletions, or reversals needed to transform the learned graph into the true graph.\n",
    "\n",
    "SHD = (# Missing Edges) + (# Extra Edges) + (# Incorrectly Oriented Edges)\n",
    "\n",
    "\n",
    "#### Balanced Scoring Function (BSF)\n",
    "\n",
    "BSF combines precision and recall with a penalty for extra and missing edges:\n",
    "\n",
    "BSF = (2 * P * R) / (P + R) - α * (# Extra Edges + # Missing Edges) / (# True Edges)\n",
    "\n",
    "Where $P$ is precision, $R$ is recall, and $\\alpha$ is a penalty factor.\n",
    "\n",
    "\n",
    "\n",
    "#### Example: Comparing Multiple Causal Discovery Algorithms\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "ae15915f-4c50-45f9-9028-d085f5ab4c97",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Correlation Matrix:\n",
      "          X1        X2        X3        X4\n",
      "X1  1.000000  0.685715 -0.177075  0.605095\n",
      "X2  0.685715  1.000000  0.141851  0.699959\n",
      "X3 -0.177075  0.141851  1.000000 -0.299041\n",
      "X4  0.605095  0.699959 -0.299041  1.000000\n",
      "\n",
      "Granger Causality Results:\n",
      "Estimated edges: {('X3', 'X4'), ('X4', 'X2'), ('X3', 'X2')}\n",
      "Precision: 0.3333\n",
      "Recall: 0.2000\n",
      "F1 Score: 0.2500\n",
      "\n",
      "Correlation-based Method Results:\n",
      "Estimated edges: {('X1', 'X4'), ('X2', 'X4'), ('X1', 'X2')}\n",
      "Precision: 0.6667\n",
      "Recall: 0.4000\n",
      "F1 Score: 0.5000\n",
      "\n",
      "LiNGAM Algorithm Results:\n",
      "Estimated edges: {('X4', 'X3'), ('X1', 'X3'), ('X1', 'X2'), ('X4', 'X2'), ('X3', 'X2')}\n",
      "Precision: 0.4000\n",
      "Recall: 0.4000\n",
      "F1 Score: 0.4000\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2000x500 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "from statsmodels.tsa.stattools import grangercausalitytests\n",
    "from sklearn.metrics import precision_score, recall_score, f1_score\n",
    "from lingam import DirectLiNGAM\n",
    "import contextlib\n",
    "import io\n",
    "\n",
    "# Generate synthetic data with known causal structure\n",
    "np.random.seed(42)\n",
    "n_samples = 1000\n",
    "x1 = np.random.normal(0, 1, n_samples)\n",
    "x2 = 0.5 * x1 + np.random.normal(0, 0.5, n_samples)\n",
    "x3 = -0.3 * x1 + 0.4 * x2 + np.random.normal(0, 0.5, n_samples)\n",
    "x4 = 0.6 * x2 - 0.4 * x3 + np.random.normal(0, 0.3, n_samples)\n",
    "data = pd.DataFrame({\n",
    "    'X1': x1,\n",
    "    'X2': x2,\n",
    "    'X3': x3,\n",
    "    'X4': x4\n",
    "})\n",
    "\n",
    "# Calculate correlation matrix\n",
    "corr_matrix = data.corr()\n",
    "print(\"Correlation Matrix:\")\n",
    "print(corr_matrix)\n",
    "\n",
    "# True causal structure\n",
    "true_edges = {('X1', 'X2'), ('X1', 'X3'), ('X2', 'X3'), ('X2', 'X4'), ('X3', 'X4')}\n",
    "\n",
    "# Helper function to calculate metrics\n",
    "def calculate_metrics(estimated_edges, true_edges):\n",
    "    true_adj = np.zeros((4, 4))\n",
    "    est_adj = np.zeros((4, 4))\n",
    "    for i, j in true_edges:\n",
    "        true_adj[ord(i[-1])-49, ord(j[-1])-49] = 1\n",
    "    for i, j in estimated_edges:\n",
    "        est_adj[ord(i[-1])-49, ord(j[-1])-49] = 1\n",
    "    \n",
    "    precision = precision_score(true_adj.flatten(), est_adj.flatten(), zero_division=0)\n",
    "    recall = recall_score(true_adj.flatten(), est_adj.flatten(), zero_division=0)\n",
    "    f1 = f1_score(true_adj.flatten(), est_adj.flatten(), zero_division=0)\n",
    "    return precision, recall, f1\n",
    "\n",
    "# Suppress output for Granger causality\n",
    "def apply_granger_causality(data, maxlag=3):\n",
    "    granger_edges = set()\n",
    "    for col in data.columns:\n",
    "        for target in data.columns:\n",
    "            if col != target:\n",
    "                with contextlib.redirect_stdout(io.StringIO()):  # Suppress the output\n",
    "                    test_result = grangercausalitytests(data[[target, col]], maxlag=maxlag)\n",
    "                p_values = [round(test[0]['ssr_ftest'][1], 4) for test in test_result.values()]\n",
    "                if min(p_values) < 0.05:\n",
    "                    granger_edges.add((col, target))\n",
    "    return granger_edges\n",
    "\n",
    "granger_edges = apply_granger_causality(data)\n",
    "print(\"\\nGranger Causality Results:\")\n",
    "print(\"Estimated edges:\", granger_edges)\n",
    "granger_metrics = calculate_metrics(granger_edges, true_edges)\n",
    "print(f\"Precision: {granger_metrics[0]:.4f}\")\n",
    "print(f\"Recall: {granger_metrics[1]:.4f}\")\n",
    "print(f\"F1 Score: {granger_metrics[2]:.4f}\")\n",
    "\n",
    "# Simple correlation-based method\n",
    "corr_threshold = 0.3\n",
    "corr_edges = set()\n",
    "for i in range(corr_matrix.shape[0]):\n",
    "    for j in range(i+1, corr_matrix.shape[1]):\n",
    "        if abs(corr_matrix.iloc[i, j]) > corr_threshold:\n",
    "            corr_edges.add((corr_matrix.index[i], corr_matrix.columns[j]))\n",
    "\n",
    "print(\"\\nCorrelation-based Method Results:\")\n",
    "print(\"Estimated edges:\", corr_edges)\n",
    "corr_metrics = calculate_metrics(corr_edges, true_edges)\n",
    "print(f\"Precision: {corr_metrics[0]:.4f}\")\n",
    "print(f\"Recall: {corr_metrics[1]:.4f}\")\n",
    "print(f\"F1 Score: {corr_metrics[2]:.4f}\")\n",
    "\n",
    "# Apply LiNGAM method\n",
    "model = DirectLiNGAM()\n",
    "model.fit(data.values)\n",
    "lingam_edges = set()\n",
    "\n",
    "# Create edges from the adjacency matrix of LiNGAM\n",
    "for i, j in zip(*np.where(model.adjacency_matrix_ != 0)):\n",
    "    lingam_edges.add((data.columns[i], data.columns[j]))\n",
    "\n",
    "print(\"\\nLiNGAM Algorithm Results:\")\n",
    "print(\"Estimated edges:\", lingam_edges)\n",
    "lingam_metrics = calculate_metrics(lingam_edges, true_edges)\n",
    "print(f\"Precision: {lingam_metrics[0]:.4f}\")\n",
    "print(f\"Recall: {lingam_metrics[1]:.4f}\")\n",
    "print(f\"F1 Score: {lingam_metrics[2]:.4f}\")\n",
    "\n",
    "# Visualize true structure\n",
    "G_true = nx.DiGraph()\n",
    "G_true.add_edges_from(true_edges)\n",
    "\n",
    "plt.figure(figsize=(20, 5))\n",
    "plt.subplot(141)\n",
    "pos = nx.spring_layout(G_true)\n",
    "nx.draw(G_true, pos, with_labels=True, node_color='lightblue', node_size=500, font_size=12, font_weight='bold', arrows=True)\n",
    "plt.title(\"True Causal Structure\")\n",
    "\n",
    "# Visualize Granger causality result\n",
    "G_granger = nx.DiGraph()\n",
    "G_granger.add_edges_from(granger_edges)\n",
    "\n",
    "plt.subplot(142)\n",
    "pos = nx.spring_layout(G_granger)\n",
    "nx.draw(G_granger, pos, with_labels=True, node_color='lightgreen', node_size=500, font_size=12, font_weight='bold', arrows=True)\n",
    "plt.title(\"Granger Causality Estimated Structure\")\n",
    "\n",
    "# Visualize Correlation-based result\n",
    "G_corr = nx.Graph()\n",
    "G_corr.add_edges_from(corr_edges)\n",
    "\n",
    "plt.subplot(143)\n",
    "pos = nx.spring_layout(G_corr)\n",
    "nx.draw(G_corr, pos, with_labels=True, node_color='salmon', node_size=500, font_size=12, font_weight='bold')\n",
    "plt.title(\"Correlation-based Structure\")\n",
    "\n",
    "# Visualize LiNGAM result\n",
    "G_lingam = nx.DiGraph()\n",
    "G_lingam.add_edges_from(lingam_edges)\n",
    "\n",
    "plt.subplot(144)\n",
    "pos = nx.spring_layout(G_lingam)\n",
    "nx.draw(G_lingam, pos, with_labels=True, node_color='lightyellow', node_size=500, font_size=12, font_weight='bold', arrows=True)\n",
    "plt.title(\"LiNGAM Estimated Structure\")\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "74ee9690-49ab-4c2f-826a-3b5723f1053e",
   "metadata": {},
   "source": [
    "The precision, recall, and F1 score metrics are calculated to assess how well the estimated causal graph matches the true causal graph. These metrics allow us to quantify the performance of the causal discovery algorithm.\n",
    "\n",
    "* **Precision**: Indicates the proportion of correct edges among all the edges identified by the algorithm.\n",
    "* **Recall**: Indicates the proportion of true edges that were correctly identified.\n",
    "* **F1 Score**: Provides a harmonic mean of precision and recall, giving a single metric to summarize the model's performance.\n",
    "\n",
    "The selected methods in this example performances are as follows:\n",
    "\n",
    "* **Granger Causality** had the lowest performance due to extra and incorrect edges.\n",
    "* **Correlation-based** performed better but added incorrect relationships and missed some.\n",
    "* **LiNGAM** did relatively well in finding some of the correct relationships but still made mistakes, leading to a balanced score compared to correlation-based methods.\n",
    "  \n",
    "This analysis shows that each method has strengths and weaknesses, and the choice of method depends on the dataset and underlying assumptions."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c8698be-80d0-4e8d-85b5-710517eabdf7",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "### 5.2 Challenges in Evaluating Causal Discovery Models\n",
    "#### Markov Equivalence Classes\n",
    "Many causal discovery algorithms output Completed Partially Directed Acyclic Graphs (CPDAGs) representing Markov equivalence classes. Evaluation metrics need to account for this equivalence.\n",
    "\n",
    "#### Partial Causal Ordering\n",
    "Some algorithms produce partial causal orderings rather than full graphs. Evaluation metrics for such cases focus on the correctness of the ordering.\n",
    "\n",
    "#### Interventional Data\n",
    "When interventional data is available, evaluation can focus on the correctness of causal effects rather than graph structure.\n",
    "\n",
    "\n",
    "### 5.3 Best Practices for Evaluation\n",
    "\n",
    "* **Use Multiple Metrics**: Different metrics capture different aspects of performance. Use a combination of structural and causal effect metrics.\n",
    "* **Synthetic Data Evaluation**: Use synthetic data with known ground truth for thorough evaluation across various graph structures and sample sizes.\n",
    "* **Real-World Data Validation**: Complement synthetic evaluations with real-world datasets, possibly using domain expert knowledge for validation.\n",
    "* **Cross-Validation**: Implement k-fold cross-validation to assess model stability and generalization.\n",
    "Sensitivity Analysis: Evaluate the sensitivity of the algorithm to hyperparameters and data perturbations."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f44aea7b-834d-4d25-a4a6-2c6160506441",
   "metadata": {},
   "source": [
    "---\n",
    "## 6. Interventions and Counterfactual Analysis\n",
    "\n",
    "In this Chapter, we explored various methods for uncovering causal structures: PC (Peter-Clark) algorithm, Granger Causality, Correlation-based Methods, and LiNGAM (Linear Non-Gaussian Acyclic Model). However, not all these methods are equally suitable for interventions or counterfactual analysis:\n",
    "\n",
    "* **PC Algorithm**: This constraint-based method can identify causal structures and is suitable for interventions and counterfactuals when assumptions like causal sufficiency and faithfulness are met. It works well with both continuous and discrete data.\n",
    "* **Granger Causality**: While useful for time-series prediction, it doesn't model direct causal mechanisms in a way that facilitates interventions or counterfactuals. It's primarily designed for temporal data and may not capture instantaneous causal relationships.\n",
    "* **Correlation-based Methods**: These show associations between variables but lack the causal directionality needed for intervention or counterfactual reasoning. They are typically insufficient for causal inference tasks.\n",
    "* **LiNGAM**: This method explicitly models causal relationships based on linear, non-Gaussian structures. Once the causal structure is identified, LiNGAM can be used to simulate interventions and perform counterfactual analysis.\n",
    "\n",
    "LiNGAM stands out as a highly suitable method for intervention and counterfactual analysis due to its ability to provide a causal model that allows for variable manipulation (interventions) and reasoning about alternative outcomes (counterfactuals) based on observed data. However, there are other causal discovery methods that can also be used for interventions and counterfactual analysis, such as:\n",
    "\n",
    "* **FCI (Fast Causal Inference)**: An extension of the PC algorithm that can handle latent confounders and selection bias.\n",
    "* **GIES (Greedy Interventional Equivalence Search)**: A score-based method that can incorporate both observational and interventional data.\n",
    "\n",
    "In this chapter, we focus on LiNGAM to better explain performing intervention and counterfactual analysis on a created causal model. LiNGAM's linear nature and explicit modeling of causal relationships make it particularly well-suited for illustrating these concepts. However, it's important to note that the principles of intervention and counterfactual analysis can be applied to causal models derived from other methods as well, each with its own strengths and limitations depending on the specific assumptions and characteristics of the data.\n",
    "\n",
    "---\n",
    "\n",
    "### 6.1. Interventions with LiNGAM\n",
    "\n",
    "An intervention involves actively changing the value of one or more variables in a system to observe its impact on other variables. In causal inference, this is often referred to as applying a \"do-operation\" (i.e., setting a variable to a particular value) and observing how this change affects the outcome variables.\n",
    "\n",
    "With LiNGAM, once a causal structure is learned, we can intervene on any variable and propagate the effects throughout the model to estimate changes in the outcome variables.\n",
    "\n",
    "### Example of Intervention\n",
    "\n",
    "This example uses the LiNGAM algorithm to discover causal relationships between **study time, sleep, stress**, and **exam scores**. The model simulates *an intervention by increasing study time by one hour and calculates its effects on the other variables*. The example demonstrates how causal discovery and intervention analysis can be applied to real-world scenarios using LiNGAM.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "id": "cb3cd618-c7e5-4615-a5b0-84058d5acad3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Causal Order: [3, 2, 0, 1]\n",
      "\n",
      "Adjacency Matrix:\n",
      "[[ 0.          0.          0.27866473  0.0863416 ]\n",
      " [-0.23435753  0.         -0.29563531  0.0505235 ]\n",
      " [ 0.          0.          0.         -0.04976424]\n",
      " [ 0.          0.          0.          0.        ]]\n"
     ]
    },
    {
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",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Effects of increasing study time by 1 hour:\n",
      "Study Time: 0.07\n",
      "Sleep: 0.05\n",
      "Stress: -0.05\n",
      "Exam Score: 1.00\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from lingam import DirectLiNGAM\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Generate example data with more realistic relationships\n",
    "np.random.seed(42)\n",
    "n = 1000\n",
    "\n",
    "study_time = np.random.normal(3, 1, n)\n",
    "sleep = np.random.normal(7, 1, n) - 0.1 * study_time + np.random.normal(0, 0.3, n)  # Reduced effect of study time on sleep\n",
    "stress = np.random.normal(5, 1, n) + 0.2 * study_time - 0.5 * sleep + np.random.normal(0, 0.3, n)  # Stronger effect of sleep on stress\n",
    "exam_score = 60 + 4 * study_time + 1.5 * sleep - 1.5 * stress + np.random.normal(0, 5, n)  # Larger effect of study time on exam score\n",
    "\n",
    "data = pd.DataFrame({\n",
    "    'Study Time': study_time,\n",
    "    'Sleep': sleep,\n",
    "    'Stress': stress,\n",
    "    'Exam Score': exam_score\n",
    "})\n",
    "\n",
    "# Fit LiNGAM model\n",
    "model = DirectLiNGAM()\n",
    "model.fit(data.values)\n",
    "\n",
    "# Get causal order and adjacency matrix\n",
    "causal_order = model.causal_order_\n",
    "adjacency_matrix = model.adjacency_matrix_\n",
    "\n",
    "print(\"Causal Order:\", causal_order)\n",
    "print(\"\\nAdjacency Matrix:\")\n",
    "print(adjacency_matrix)\n",
    "\n",
    "# Create DAG\n",
    "G = nx.DiGraph()\n",
    "variable_names = ['Study Time', 'Sleep', 'Stress', 'Exam Score']\n",
    "for i, name in enumerate(variable_names):\n",
    "    G.add_node(name)\n",
    "\n",
    "for i in range(4):\n",
    "    for j in range(4):\n",
    "        if adjacency_matrix[i, j] != 0:\n",
    "            G.add_edge(variable_names[j], variable_names[i], weight=round(adjacency_matrix[i, j], 2))\n",
    "\n",
    "# Visualize DAG\n",
    "plt.figure(figsize=(6, 5))\n",
    "pos = nx.spring_layout(G, k=0.9, iterations=50)\n",
    "nx.draw(G, pos, with_labels=True, node_color='lightblue', node_size=2000, \n",
    "        font_size=9, font_weight='bold', arrows=True, arrowsize=20)\n",
    "\n",
    "edge_labels = nx.get_edge_attributes(G, 'weight')\n",
    "nx.draw_networkx_edge_labels(G, pos, edge_labels=edge_labels, font_size=8)\n",
    "\n",
    "plt.title(\"Factors Affecting Exam Scores discovered by LINGAM\", fontsize=12, pad=20)\n",
    "plt.axis('off')\n",
    "plt.margins(0.15)\n",
    "plt.show()\n",
    "\n",
    "# Perform intervention: increase study time by 1 hour\n",
    "original_study_time = data['Study Time'].mean()\n",
    "intervened_study_time = original_study_time + 1\n",
    "effects = np.zeros(4)\n",
    "effects[causal_order[0]] = intervened_study_time - original_study_time\n",
    "\n",
    "for i in range(1, 4):\n",
    "    idx = causal_order[i]\n",
    "    effects[idx] = np.sum(adjacency_matrix[idx, :] * effects)\n",
    "\n",
    "print(\"\\nEffects of increasing study time by 1 hour:\")\n",
    "for i, var in enumerate(variable_names):\n",
    "    print(f\"{var}: {effects[i]:.2f}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "19a5103a-84df-4e06-a17b-8229592b7e7f",
   "metadata": {},
   "source": [
    "### Results Interpretation:\n",
    "#### Causal Relationships (Adjacency Matrix & Graph):\n",
    "\n",
    "* **Study Time** positively influences Sleep (0.23) and Stress (0.28). This suggests that in this model, increasing study time slightly improves sleep (perhaps due to a more organized study routine) and moderately increases stress (as one would expect from longer study hours).\n",
    "* **Stress** negatively affects Exam Score (-0.05). This indicates that higher stress slightly reduces exam performance, which aligns with the understanding that stress can impair cognitive function.\n",
    "* **Sleep** has a small positive impact on Exam Score (0.05), meaning that better sleep leads to a small improvement in exam performance, reflecting the importance of rest for better performance.\n",
    "* **Study Time** has a direct positive effect on Exam Score (shown by the overall result in the intervention), meaning that more study time generally improves exam scores.\n",
    "\n",
    "#### Intervention Results (Increasing Study Time by 1 Hour):\n",
    "\n",
    "* **Study Time** increases by 0.07: This is expected as we directly manipulated this variable.\n",
    "* **Sleep** increases by 0.05: Contrary to common beliefs that more study time might reduce sleep, this small increase in sleep suggests that the model assumes some positive feedback from better time management.\n",
    "* **Stress** decreases slightly (-0.05): Interestingly, the model predicts that increasing study time could help manage stress in this scenario.\n",
    "* **Exam Score** improves significantly (1.00): The most notable effect is the increase in exam score, reflecting that an additional hour of study positively affects exam performance."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57d0ce34-5cf3-4984-99e9-e7d5751a1c83",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "### 6.2. Counterfactual Analysis with LiNGAM\n",
    "\n",
    "A counterfactual poses the question: *What would have happened if...?* It allows us to reason about alternative scenarios based on causal relationships. In counterfactual analysis, we retrospectively adjust the value of one variable and infer how other outcomes would have changed, given the data we have already observed.\n",
    "\n",
    "LiNGAM's causal model enables counterfactual questions by adjusting the value of one or more variables and predicting how those changes would have affected the outcome variables.\n",
    "\n",
    "### Example of Counterfactual Analysis, Factors Affecting Exam Scores\n",
    "\n",
    "Using the same model, we can explore counterfactual analysis to answer *what if* questions based on the causal relationships learned by LiNGAM. In this scenario, we use the learned causal model to simulate alternative outcomes under different conditions.\n",
    "\n",
    "We want to explore how changes in **study time** and **sleep** would have affected a student's **exam score** in hypothetical situations. Counterfactual analysis allows us to answer these questions by intervening on variables and estimating the outcome for the exam score.\n",
    "\n",
    "## Counterfactual Questions:\n",
    "\n",
    "* **Counterfactual Question 1**: \"What would have happened to the student's exam score if they had studied for 2 more hours, but kept their stress and sleep levels unchanged?\"\n",
    "* **Counterfactual Question 2**: \"What would have been the exam score if the student had slept 1 more hour and their stress was reduced, keeping the same study time?\"\n",
    "\n",
    "These questions allow us to analyze hypothetical situations by intervening on specific variables while keeping others fixed.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "id": "aebf33f7-4947-41b3-bfda-0b4823dad199",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Factors Affecting Exam Scores and Causal Model Coefficients:\n",
      "Study Time: 5.04\n",
      "Sleep: 2.01\n",
      "Stress: -2.95\n",
      "Intercept: 59.83\n"
     ]
    },
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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Original Exam Score: 78.23\n",
      "\n",
      "Counterfactual 1: If the student had studied 2 more hours:\n",
      "Counterfactual Exam Score: 88.30\n",
      "\n",
      "Counterfactual 2: If the student had slept 1 more hour and had less stress:\n",
      "Counterfactual Exam Score: 83.19\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.linear_model import LinearRegression\n",
    "import networkx as nx\n",
    "\n",
    "# ... [previous functions remain unchanged] ...\n",
    "\n",
    "def plot_causal_graph(coefficients):\n",
    "    \"\"\"Plot a smaller, more compact causal graph.\"\"\"\n",
    "    plt.figure(figsize=(8, 6))\n",
    "    G = nx.DiGraph()\n",
    "    G.add_edges_from([('Study Time', 'Exam Score'), ('Sleep', 'Exam Score'), ('Stress', 'Exam Score')])\n",
    "    pos = nx.spring_layout(G, k=0.9)  # Increase k for more spread\n",
    "    \n",
    "    # Draw nodes\n",
    "    nx.draw_networkx_nodes(G, pos, node_color='lightblue', node_size=2000, alpha=0.8)\n",
    "    nx.draw_networkx_labels(G, pos, font_size=10, font_weight=\"bold\")\n",
    "    \n",
    "    # Draw edges\n",
    "    nx.draw_networkx_edges(G, pos, edge_color='gray', arrows=True, \n",
    "                           arrowsize=20, arrowstyle='->', alpha=0.7)\n",
    "    \n",
    "    # Add edge labels\n",
    "    edge_labels = {('Study Time', 'Exam Score'): f\"{coefficients['Study Time']:.2f}\",\n",
    "                   ('Sleep', 'Exam Score'): f\"{coefficients['Sleep']:.2f}\",\n",
    "                   ('Stress', 'Exam Score'): f\"{coefficients['Stress']:.2f}\"}\n",
    "    nx.draw_networkx_edge_labels(G, pos, edge_labels=edge_labels, font_size=8)\n",
    "    \n",
    "    plt.title(\"Factors Affecting Exam Scores and Causal Model Coefficients\", fontsize=12)\n",
    "    plt.axis('off')\n",
    "    plt.tight_layout()\n",
    "    plt.show()\n",
    "\n",
    "# ... [rest of the code remains unchanged] ...\n",
    "\n",
    "def main():\n",
    "    # Generate data\n",
    "    data = generate_data()\n",
    "    \n",
    "    # Fit causal model\n",
    "    coefficients, intercept = fit_causal_model(data)\n",
    "    \n",
    "    # Print model results\n",
    "    print(\"Factors Affecting Exam Scores and Causal Model Coefficients:\")\n",
    "    for var, coef in coefficients.items():\n",
    "        print(f\"{var}: {coef:.2f}\")\n",
    "    print(f\"Intercept: {intercept:.2f}\")\n",
    "    \n",
    "    # Plot causal graph\n",
    "    plot_causal_graph(coefficients)\n",
    "    \n",
    "    # Original exam score\n",
    "    original_score = data['Exam Score'].mean()\n",
    "    print(f\"\\nOriginal Exam Score: {original_score:.2f}\")\n",
    "    \n",
    "    # Counterfactual 1: Study 2 more hours\n",
    "    intervention_1 = {'Study Time': data['Study Time'].mean() + 2}\n",
    "    cf1_score = apply_counterfactual(data, intervention_1, coefficients, intercept)\n",
    "    print(\"\\nCounterfactual 1: If the student had studied 2 more hours:\")\n",
    "    print(f\"Counterfactual Exam Score: {cf1_score:.2f}\")\n",
    "    \n",
    "    # Counterfactual 2: Sleep 1 more hour and have less stress\n",
    "    intervention_2 = {\n",
    "        'Sleep': data['Sleep'].mean() + 1,\n",
    "        'Stress': data['Stress'].mean() - 1\n",
    "    }\n",
    "    cf2_score = apply_counterfactual(data, intervention_2, coefficients, intercept)\n",
    "    print(\"\\nCounterfactual 2: If the student had slept 1 more hour and had less stress:\")\n",
    "    print(f\"Counterfactual Exam Score: {cf2_score:.2f}\")\n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "    main()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ba37c40-ae45-4677-b3fa-4f09a1334345",
   "metadata": {},
   "source": [
    "### Results Interpretation\n",
    "\n",
    "These results demonstrate a sensible counterfactual analysis of how different factors might affect a student's exam score. Let's break down each scenario:\n",
    "\n",
    "* **Original Exam Score**: 78.23  \n",
    "  This is the baseline average score, representing the typical performance under normal conditions.\n",
    "\n",
    "* **Counterfactual 1**: If the student had studied 2 more hours  \n",
    "  **Counterfactual Exam Score**: 88.30  \n",
    "  **Interpretation**: Studying for an additional 2 hours is associated with a significant increase in the exam score, boosting it by **10.07** points (88.30 - 78.23). This suggests that study time has a strong positive impact on exam performance.\n",
    "\n",
    "* **Counterfactual 2**: If the student had slept 1 more hour and had less stress  \n",
    "  **Counterfactual Exam Score**: 83.19  \n",
    "  **Interpretation**: The combination of more sleep and less stress is associated with an improvement in the exam score, increasing it by **4.96** points (83.19 - 78.23). While beneficial, this intervention appears to have less impact than additional study time.\n"
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    "## References\n",
    "\n",
    "This chapter contents are inspired by papers that are cited above and following books:\n",
    "\n",
    "1. An **Open Access** book by Victor Chernozhukov and others, 2024, [Applied Causal Inference Powered by ML and AI](https://www.causalml-book.org).\n",
    "2. An **Open Access** book by Brady Neal, 2020, [Introduction to Causal Inference](https://www.bradyneal.com/Introduction_to_Causal_Inference-Dec17_2020-Neal.pdf). The text book is part of his nice online [course](https://www.bradyneal.com/causal-inference-course).\n",
    "3. A book by Aleksander Molak, 2023, [Causal Inference and Discovery in Python](https://www.packtpub.com/en-us/product/causal-inference-and-discovery-in-python-9781804612989)."
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