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   "source": [
    "# PHASE 1: EXPLAIN & BREAKDOWN (LEARNING PHASE)\n",
    "\n",
    "## Simple Explanation of Bayesian Networks\n",
    "\n",
    "Bayesian Networks are probabilistic graphical models that represent relationships between variables using directed graphs (like flowcharts with arrows). Think of them as \"smart decision trees\" that capture how different factors influence each other using probability. Each node represents a variable (like \"Rain,\" \"Traffic,\" or \"Late to Work\"), and arrows show direct influences. The network uses Bayes' theorem to calculate the probability of events given evidence. For example, if you know it's raining, the network can predict how likely you are to be late to work by considering intermediate factors like traffic. They're powerful for reasoning under uncertainty, making predictions, and understanding cause-and-effect relationships in complex systems.\n",
    "\n",
    "## Detailed Learning Roadmap\n",
    "\n",
    "### 1. **Graph Theory Foundations**\n",
    "   - **Directed Acyclic Graphs (DAGs)**: Learn about nodes, edges, and why cycles aren't allowed\n",
    "   - **Example**: Family tree showing parent-child relationships (parents → children, no loops)\n",
    "\n",
    "### 2. **Probability Fundamentals**\n",
    "   - **Joint, Marginal, and Conditional Probability**: Understanding P(A,B), P(A), and P(A|B)\n",
    "   - **Example**: P(Rain, Traffic) vs P(Rain) vs P(Traffic|Rain)\n",
    "\n",
    "### 3. **Conditional Independence**\n",
    "   - **D-separation rules**: When variables are independent given evidence\n",
    "   - **Example**: \"Wet grass\" depends on \"Rain\" and \"Sprinkler,\" but Rain and Sprinkler are independent\n",
    "\n",
    "### 4. **Network Construction**\n",
    "   - **Structure Learning**: Building the graph from data or expert knowledge\n",
    "   - **Example**: Medical diagnosis network connecting symptoms to diseases\n",
    "\n",
    "### 5. **Parameter Learning**\n",
    "   - **Conditional Probability Tables (CPTs)**: Learning probabilities for each node\n",
    "   - **Example**: P(Fever=High|Disease=Flu) = 0.8\n",
    "\n",
    "### 6. **Inference Methods**\n",
    "   - **Exact Inference**: Variable elimination, junction tree algorithms\n",
    "   - **Example**: Calculating P(Disease|Symptoms) using all available evidence\n",
    "\n",
    "### 7. **Approximate Inference**\n",
    "   - **Sampling Methods**: Monte Carlo, Gibbs sampling\n",
    "   - **Example**: Estimating probabilities when exact calculation is too complex\n",
    "\n",
    "### 8. **Dynamic Bayesian Networks**\n",
    "   - **Temporal Modeling**: Adding time dimension to capture sequences\n",
    "   - **Example**: Stock price prediction considering previous days' data\n",
    "\n",
    "## FORMULA MEMORY AIDS SECTION\n",
    "\n",
    "### 1. Bayes' Theorem\n",
    "**FORMULA**: P(A|B) = P(B|A) × P(A) / P(B)\n",
    "\n",
    "**REAL-LIFE ANALOGY**: \"Medical Test Accuracy\"\n",
    "- P(A|B) = Probability you have the disease given a positive test (what you want to know)\n",
    "- P(B|A) = Test accuracy - probability of positive test given you have disease (95%)\n",
    "- P(A) = How common the disease is in population (1 in 1000 people)\n",
    "- P(B) = How often anyone tests positive (including false positives)\n",
    "\n",
    "**MEMORY TRICK**: \"Bayes flips the question! From 'test accuracy' to 'do I really have it?'\"\n",
    "\n",
    "### 2. Chain Rule of Probability\n",
    "**FORMULA**: P(X₁, X₂, ..., Xₙ) = ∏ᵢ P(Xᵢ|Parents(Xᵢ))\n",
    "\n",
    "**REAL-LIFE ANALOGY**: \"Recipe Steps Dependencies\"\n",
    "- X₁ = \"Buy ingredients\" (depends on nothing: P(X₁))\n",
    "- X₂ = \"Preheat oven\" (depends on having ingredients: P(X₂|X₁))\n",
    "- X₃ = \"Bake cake\" (depends on oven being hot: P(X₃|X₂))\n",
    "- Total probability = P(X₁) × P(X₂|X₁) × P(X₃|X₂)\n",
    "\n",
    "**MEMORY TRICK**: \"Chain rule = Chain of cooking steps - each step depends on previous ones!\"\n",
    "\n",
    "### 3. Conditional Independence\n",
    "**FORMULA**: P(X|Y,Z) = P(X|Z) if X ⊥ Y | Z\n",
    "\n",
    "**REAL-LIFE ANALOGY**: \"Weather and Clothing Choice\"\n",
    "- X = \"Wearing jacket\" \n",
    "- Y = \"Season (Winter/Summer)\"\n",
    "- Z = \"Today's temperature\"\n",
    "- Given today's temperature, the season doesn't matter for jacket choice\n",
    "\n",
    "**MEMORY TRICK**: \"Given the 'middleman' (Z), the other factor (Y) becomes irrelevant!\"\n",
    "\n",
    "## Step-by-Step Numerical Example\n",
    "\n",
    "Let's build a simple medical diagnosis network:\n",
    "\n",
    "**Variables**: \n",
    "- Flu (F): Yes/No\n",
    "- Fever (Fv): High/Normal  \n",
    "- Cough (C): Yes/No\n",
    "\n",
    "**Network Structure**: Flu → Fever, Flu → Cough\n",
    "\n",
    "**Step 1: Prior Probabilities**\n",
    "- P(Flu = Yes) = 0.1\n",
    "- P(Flu = No) = 0.9\n",
    "\n",
    "**Step 2: Conditional Probability Tables**\n",
    "- P(Fever = High | Flu = Yes) = 0.8\n",
    "- P(Fever = High | Flu = No) = 0.1\n",
    "- P(Cough = Yes | Flu = Yes) = 0.7\n",
    "- P(Cough = Yes | Flu = No) = 0.2\n",
    "\n",
    "**Step 3: Calculate Joint Probability**\n",
    "P(Flu=Yes, Fever=High, Cough=Yes) = P(Flu=Yes) × P(Fever=High|Flu=Yes) × P(Cough=Yes|Flu=Yes)\n",
    "= 0.1 × 0.8 × 0.7 = 0.056\n",
    "\n",
    "**Step 4: Inference with Evidence**\n",
    "Given evidence (Fever=High, Cough=Yes), calculate P(Flu=Yes|Evidence):\n",
    "\n",
    "P(Flu=Yes|Fv=High,C=Yes) = P(Fv=High,C=Yes|Flu=Yes) × P(Flu=Yes) / P(Fv=High,C=Yes)\n",
    "\n",
    "Numerator = 0.8 × 0.7 × 0.1 = 0.056\n",
    "Denominator = 0.056 + P(Fv=High,C=Yes|Flu=No) × P(Flu=No)\n",
    "= 0.056 + (0.1 × 0.2 × 0.9) = 0.056 + 0.018 = 0.074\n",
    "\n",
    "Result: P(Flu=Yes|Evidence) = 0.056/0.074 = 0.757 (75.7%)\n",
    "\n",
    "## Real-World AI Use Case\n",
    "\n",
    "**Medical Diagnosis Systems**: IBM Watson for Oncology uses Bayesian Networks to assist doctors in cancer diagnosis and treatment recommendations. The network incorporates patient symptoms, medical history, test results, and treatment outcomes to calculate probabilities of different diagnoses and suggest optimal treatment plans. It processes thousands of medical papers and patient cases to update its probability estimates continuously.\n",
    "\n",
    "## Tips for Mastering Bayesian Networks\n",
    "\n",
    "1. **Practice Sources**: \n",
    "   - Kevin Murphy's \"Machine Learning: A Probabilistic Perspective\"\n",
    "   - Online courses: Stanford CS228 (Probabilistic Graphical Models)\n",
    "   - Kaggle datasets for hands-on practice\n",
    "\n",
    "2. **Programming Practice**:\n",
    "   - Start with pgmpy library in Python\n",
    "   - Work through medical diagnosis examples\n",
    "   - Build weather prediction networks\n",
    "\n",
    "3. **Problem-Solving Strategy**:\n",
    "   - Always draw the network first\n",
    "   - Identify independence assumptions\n",
    "   - Work through small examples by hand before coding\n",
    "   - Practice different inference scenarios\n",
    "\n",
    "4. **Common Pitfalls to Avoid**:\n",
    "   - Don't create cycles in your graphs\n",
    "   - Remember that correlation doesn't imply causation\n",
    "   - Be careful about the direction of arrows (causality)\n",
    "   - Test your independence assumptions with data"
   ]
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  {
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   "execution_count": 2,
   "id": "ef70f8f5-c8b7-4646-81bc-8a5d6c7c34dd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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     ]
    }
   ],
   "source": [
    "# Installation commands for Google Colab and local Mac\n",
    "!pip install pgmpy pandas numpy matplotlib seaborn scikit-learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "a814731a-bf98-4282-91e3-3d734a911fb8",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:__main__:Starting Bayesian Network implementation\n",
      "INFO:__main__:Loading and preparing Iris dataset for Bayesian Network\n",
      "INFO:__main__:Original dataset shape: (150, 5)\n",
      "INFO:__main__:Features: ['sepal length (cm)', 'sepal width (cm)', 'petal length (cm)', 'petal width (cm)', 'species']\n",
      "INFO:__main__:Discretized sepal length (cm) -> Sepal_Length: 3 bins\n",
      "INFO:__main__:Discretized sepal width (cm) -> Sepal_Width: 3 bins\n",
      "INFO:__main__:Discretized petal length (cm) -> Petal_Length: 3 bins\n",
      "INFO:__main__:Discretized petal width (cm) -> Petal_Width: 3 bins\n",
      "INFO:__main__:Final processed dataset shape: (150, 5)\n",
      "INFO:__main__:Species distribution: {0: 50, 1: 50, 2: 50}\n",
      "INFO:__main__:Creating Bayesian Network structure\n",
      "INFO:__main__:Network nodes: ['Species', 'Sepal_Length', 'Sepal_Width', 'Petal_Length', 'Petal_Width']\n",
      "INFO:__main__:Network edges: [('Species', 'Sepal_Length'), ('Species', 'Sepal_Width'), ('Species', 'Petal_Length'), ('Species', 'Petal_Width'), ('Petal_Length', 'Petal_Width')]\n",
      "INFO:__main__:Network structure created successfully (DAG validation will occur after parameter learning)\n",
      "INFO:__main__:Learning network parameters using Maximum Likelihood Estimation\n",
      "INFO:pgmpy: Datatype (N=numerical, C=Categorical Unordered, O=Categorical Ordered) inferred from data: \n",
      " {'Sepal_Length': 'N', 'Sepal_Width': 'N', 'Petal_Length': 'N', 'Petal_Width': 'N', 'Species': 'N'}\n",
      "INFO:__main__:Model validation passed - all CPDs are properly defined\n",
      "INFO:__main__:Learned Conditional Probability Distributions:\n",
      "INFO:__main__:CPD for Species:\n",
      "INFO:__main__:  Variables: ['Species']\n",
      "INFO:__main__:  Cardinality: [3]\n",
      "INFO:__main__:  Values shape: (3,)\n",
      "INFO:__main__:  Sample values: [0.33333333 0.33333333 0.33333333]\n",
      "INFO:__main__:CPD for Sepal_Length:\n",
      "INFO:__main__:  Variables: ['Sepal_Length', 'Species']\n",
      "INFO:__main__:  Cardinality: [3 3]\n",
      "INFO:__main__:  Values shape: (3, 3)\n",
      "INFO:__main__:  Sample values: [0.8  0.1  0.02 0.2  0.62]\n",
      "INFO:__main__:CPD for Sepal_Width:\n",
      "INFO:__main__:  Variables: ['Sepal_Width', 'Species']\n",
      "INFO:__main__:  Cardinality: [3 3]\n",
      "INFO:__main__:  Values shape: (3, 3)\n",
      "INFO:__main__:  Sample values: [0.02 0.54 0.38 0.22 0.36]\n",
      "INFO:__main__:CPD for Petal_Length:\n",
      "INFO:__main__:  Variables: ['Petal_Length', 'Species']\n",
      "INFO:__main__:  Cardinality: [3 3]\n",
      "INFO:__main__:  Values shape: (3, 3)\n",
      "INFO:__main__:  Sample values: [1.   0.   0.   0.   0.92]\n",
      "INFO:__main__:CPD for Petal_Width:\n",
      "INFO:__main__:  Variables: ['Petal_Width', 'Petal_Length', 'Species']\n",
      "INFO:__main__:  Cardinality: [3 3 3]\n",
      "INFO:__main__:  Values shape: (3, 3, 3)\n",
      "INFO:__main__:Performing probabilistic inference\n",
      "INFO:__main__:Inference scenario: large_petals\n",
      "INFO:__main__:Evidence: {'Petal_Length': 2, 'Petal_Width': 2}\n",
      "INFO:__main__:Results for large_petals:\n",
      "INFO:__main__:  P(Species=Setosa|Evidence) = 0.0000\n",
      "INFO:__main__:  P(Species=Versicolor|Evidence) = 0.0435\n",
      "INFO:__main__:  P(Species=Virginica|Evidence) = 0.9565\n",
      "INFO:__main__:Inference scenario: small_petals\n",
      "INFO:__main__:Evidence: {'Petal_Length': 0, 'Petal_Width': 0}\n",
      "INFO:__main__:Results for small_petals:\n",
      "INFO:__main__:  P(Species=Setosa|Evidence) = 1.0000\n",
      "INFO:__main__:  P(Species=Versicolor|Evidence) = 0.0000\n",
      "INFO:__main__:  P(Species=Virginica|Evidence) = 0.0000\n",
      "INFO:__main__:Inference scenario: medium_sepals\n",
      "INFO:__main__:Evidence: {'Sepal_Length': 1, 'Sepal_Width': 1}\n",
      "INFO:__main__:Results for medium_sepals:\n",
      "INFO:__main__:  P(Species=Setosa|Evidence) = 0.1244\n",
      "INFO:__main__:  P(Species=Versicolor|Evidence) = 0.6312\n",
      "INFO:__main__:  P(Species=Virginica|Evidence) = 0.2443\n",
      "INFO:__main__:Inference scenario: mixed_features\n",
      "INFO:__main__:Evidence: {'Sepal_Length': 2, 'Petal_Length': 0}\n",
      "INFO:__main__:Results for mixed_features:\n",
      "INFO:__main__:  P(Species=Setosa|Evidence) = nan\n",
      "INFO:__main__:  P(Species=Versicolor|Evidence) = nan\n",
      "INFO:__main__:  P(Species=Virginica|Evidence) = nan\n",
      "INFO:__main__:Evaluating model performance\n",
      "INFO:__main__:Training data shape: (105, 5)\n",
      "INFO:__main__:Test data shape: (45, 5)\n",
      "INFO:pgmpy: Datatype (N=numerical, C=Categorical Unordered, O=Categorical Ordered) inferred from data: \n",
      " {'Sepal_Length': 'N', 'Sepal_Width': 'N', 'Petal_Length': 'N', 'Petal_Width': 'N', 'Species': 'N'}\n",
      "INFO:__main__:Model accuracy on test data: 0.8444 (38/45)\n",
      "INFO:__main__:Sample predictions:\n",
      "INFO:__main__:  ✓ Actual: 2, Predicted: 2, Confidence: 0.989\n",
      "INFO:__main__:  ✓ Actual: 1, Predicted: 1, Confidence: 1.000\n",
      "INFO:__main__:  ✗ Actual: 2, Predicted: 1, Confidence: 0.530\n",
      "INFO:__main__:  ✗ Actual: 1, Predicted: 2, Confidence: 0.947\n",
      "INFO:__main__:  ✓ Actual: 2, Predicted: 2, Confidence: 0.913\n",
      "INFO:__main__:Creating visualizations\n",
      "INFO:__main__:Saved visualization as 'bayesian_network_analysis.png'\n"
     ]
    },
    {
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I/MxxZeUruzwhOqb6nHzwwQeBZdrH+jw///zzCW6vTZs2vmuuuSZkO4899pjLTPfT50OZ2mfro48+ctnuf/zxR7Idg3CZ6PHbr897/JEdbdu2PWUmurZ17NixkM+1tpVQJrq+/xkyZPCtWLEiyftIbXrkkUdClul3nI5ZYqNXAABI79TP0d9E3fQzvKc+0aBBg9wIvaioKHfTz88880ygv7R+/Xo3egApS31ojXJU31vnKLrpZ42KDD4nRMrSyNSE9r+W6TEgPcvkdRAfiDTKLm/evLnLTJ09e7abKOX555+3UaNGhWQq169fP+R5uq9sU1F28+rVq0+qZ6msUGWYbt261f7991+X7ZsUp9qeZqZX25QNrGxXZZMr81eTLSbk4MGD7n9NHnq6NGGJf9KSU1GWlTJg/Vm12p/KrlLtPGU4K/NK701ZtMEZusp41ns7cOBA2NrPyrCOP7mirrhr23LLLbfY8OHDrVy5ci6LSJN0KZs6U6ZMgexoZUTr9Xft2uUyemXDhg0uA/tc0TE7nbqmqkn/8MMP28cff2x33XWXy0RT3UfVlleNVO1LZd4ok81PIxHiTwoaf5SB6hJqwlxNAKTPhz7nqiWeEH2Otf8SotdXFn9wdoNqhCvbxD8SIz4t1+SfwfR8HR8da3/WdPw2ny59xjQa4e233w7JRjqXxyAx8du/YsUKu/HGG0OWaT+dql672u7fJ6LvsTL4wx2rEiVKuMltE6L9q9EKei///POPG7mibPP436ts2bK5//WdAwAkL/U51K9Tf9Df//C74oorPGsXTvRdw/WP4A31iZ566il3U+16Ue3tYKVKlfKodZFNo1E1Cnrq1Km2fPlyt6xy5cruXCM1zbUUicdFE7tqroBgimvo3BhIzwiiAx5QcFnBaN1UlqFTp07Wr1+/JJf72LdvnyuhoDISCU0KGDwxzrnYnr/chAKl+oOpoJ8mu1SHpl69eic9RxMZqmOj4HEwlV8JHo4nuq/lfipPcaoJCNXeYJq0UDftR3WAFfBTGxXw1LoDBgywVq1anbSdMwny+5UsWdIFMb///nu3H+677z4bOnSoG+6pQKIuOOimfap9qOC57id1Qsik0vZVaiYx6tBcfvnlgZOCm2++2R1PBXD1vy6IqOSI/9goSFy3bt2QbQQHXf0ngcG07/X+dFFDgfQhQ4bYsGHD3KRM8fkDqiktfptPh46rLpJoeK9/aG9yHIPkan+w+JPH6rsaP8iS1GOlz7wuLOmChUrVqI2aBCr+59xfisf/+wQAkDyUUKAyIevXr3eTVsf/fe8vnYbkp76nyqXp735C/dBgKrsD78UPnsN7+r2lhC7dkDqoxI4C6JoY+eqrr3bLpk2b5s79dE4ApGcE0YFUQJnJqpsd/yQoOFin+zVq1HA/16xZ0wWJlbEdrrNXpkwZ98fsqquuOuXrJ2V7otfXrWfPni4zfvz48QkG0bNkyeLek+onB3d49By1SUE2PwWgg7PuBw4caI8++qidKb1vZcEqq9r/3hTsDlcP3h9UjH9SqSwHZbC3b98+sEz3g7PIFWBUYFU31QRXPWtl9OqkdceOHa52tILtMn/+fEsOLVq0OCngHV/x4sVD7ivT/Morr3QZy7/++qsLhErhwoWtWLFi9tdff7k6/KdL71UXQXTTZ0TB+ISC6MrA0udAFzfi08UQfX60r1UvVJSZrlr1wZ+bhI5VMN3XxZT4wf8z8dNPP9l1113n6rzHH51wro/B6ahYsWKghr9f/PtnS8fq77//tpUrVyaYja79rFEAd9xxh7uvYLzWjT/aQvXSldFeoECBc9o+AEAo/Q3WyCVd1NZII7I1vaNRfP79H39EH1IPJZHo3EN9U43eiH/xiQtPKeuVV15x/W0lO+nnxCjBCylPSUAaeaqR3poDzH8OrjnZ4icbAekNQXQgBSmwqjIW+sOj4JRKQCi4qnIu8ctRTJw40Z0EXXbZZS7TVZPyvfPOO+4xBTgVdNNzFHRWcEoZR8pi0aSMuq9SIjqRUmBcExnt3bvXBbwSCmqeansKYr711lsuWKggq4LSmkwzsT+SykrWxDzBgU9NgKjJSXWVWiVtJkyY4N6/tn0m5Vz0HlUeQqVUFHDdvXu362ypvcryF02SqQCohmEq+1dZ+iqxoqDeoEGDQi44qARIdHS05c2b101Yo+xgXTTQkMEvv/zS7Q9lnosyi9SpVvBUQXtlzyuornYokKhA8IgRI9wx0Gv5Oxiny1/CRxn1utqv+/6LFGdSSsQ/lFsXFXT8FPjXJDB+CmyrQ6qTPZWpUQdJx0ijCpR1EI6Osz5nCrRqXZU+UXA7IQqwK2tZ2fvaP3o/Wl/fDQVZVRZG+1+Td+q46fuh4+yfEC0+lfDRxEPaxyqJolI+r7766jmZqEvt0udHn12VqNm8ebNbrjb7Jxc918cgqfRd1nZefPFFdyHnhx9+cBnv5zJgou+rXkPvXa+jNms4rV5Dn48KFSq4CYR0IUDfG62jk9H4QXSVryKDCACSn/pn+r2cWPIAUoZGmiX0M1IXjQTWiFGNDubCk/c06lPnpgqi6+dwdJwIontH52u66fxU58CnGlELpBteF2UHIokmvHzyySd9NWvWdJP/aTJBTejZu3fvkIkH9dXUhJuaLFGTc5QpU8ZNaBhs06ZNvnbt2vkKFCjg1ilXrpybCHPPnj0hExhq+5qoURNpPvDAA2En00xse5s3b3aTGmobmsxFEw/27dvXd/z48bDv9c8//3QTk+7evTtk+ccff+wm5PRPCvP111+f8f784YcffDfddJOvZMmSbnuFCxf2NWnSxDdjxoyQ9aZMmeImClV7YmJifBdffLHvrbfeCjw+efJk33nnnefLlCmTe29+r7/+utsP2n9q87hx4wKPad9psldtL0eOHL569er5vv/++8DjmpxTx037UpNy6jW0zxcuXBhYR6+liR8To+fEvwW38UxpslVtyz9ZZzBN6nnRRRe5fapJcK+44grfZ599FjKxaPD7kG7durnJfvR+CxYs6Lvzzjt927dvT3AiUNEktTomWj9Pnjy+xo0bBx4/ePCg+6z6P4uahHTu3LmB5ya0PU3Yq4lEdaxKlSrlGzp0aEj7gifLDKYJPDXZZjh6LKFjoOcl5zFIaGLRhNqvz3Hx4sXdZ1vfUf/EWIlNLHrDDTeEbEOvE/x+4r+WJhbu2LGjL3/+/G5CZE3w9NVXXwUe0/Y0UaomCNbvMv0eCX4NHU/9vps1a9YZ7ikAQFJdddVVvm+++cbrZuD/qQ81YMAA3/Tp05M8GT1Slvow8fu1ABJ39OhR39SpU128ITY21i37559/fHv37vW6aUCyitI/XgfyAZx8ZX3SpEnWsmVLS8uUWaxyKso8RihlVqt2vDKHVdYD3tDIAWXfJ3U+gtROE8IqU1yZ36mFhnbq95lq5QMAkpd+32reGo3o0qiv+PNgMKllylL/QvOqaISnsjVVwlClFlVHWJOBn4uyczg7Gj2nUb/+spnwnuYKa9iwoSsbqtGfSF30+0wjUjWCQ6OWVcpRE4pq5K7ujxw50usmAsnm9GYfBIDToBIxDO0KXyZEJ1AE0L3z559/urI1abl23wsvvODKE61evdqVDxo7dmxIHf/UQAEctQ0AkPxUfmvZsmWudKBKnV100UUuOOj/HylL5f/Wrl3r5pvR30LNkaIyhiohqDJoKoV3JvOi4NzRRIhPPvmkrVu3zuum4P+NGzfOnSPlyZPHBdNVglNlSY8dO+Z10/D/JVpVdlYlPHVx0O/GG290JVKB9IxMdCAVSi+Z6ACSl+r2a+JTzXmgDBDVSVedeQBA5GYIJsY/aTe8paD66NGjXWBd894weaV3dDFDI0QVoNU8R/FHb+zcudOztkUyXdRQ0pH6uRrNoaznHDlyuAtQGs2hm0ZzIOVpNLXmQ6pYsaKbF0oJPToP0THTyA59n4D0iolFgVSIa1sAkuLjjz/2ugkAgFSEIHnqvsChgKD/tnXrVleuQpN4w9tMdKQ+ZcqUsY4dO7qbaESHP6g+ePBge+qpp8hM90hcXFyCF/7+/vtvF1QH0jMy0QEAAAAgnXjvvfdcTVoFnWbNmuUC6woUli1b1m644QavmxdxZSn8QfPt27fbJZdc4oLmuqncTvysZwDhL0D98MMPLivdfwFK95HybrvtNlcSU6WpFDRfsmSJFSxY0P19KVWqlI0ZM8brJgLJhiA6AAAAAKQDmsy5b9++1r17d3vmmWfsjz/+cMPsVZtb82YokxMpJ0OGDC6opJrbd999N0HzVGrNmjUu8Kf/X375ZStUqJB988037thVrVrV6+ZFHJVuUdDcn3kefAHqiiuucGVcmHDUO8o4b9y4sRs9v2rVKlcfXf8XKFDApk+f7r4/QHpFEB0AAAAA0gHVo1WpA82rE1yrVsF0TdSnYBRSjkYE+Gs6Hzp0yC677DJ3HBQMrFWrlpsHCd7SsdEEr6q1rQCgJubVd+bZZ5+1+fPn2yeffOJ1EyP24tO9997rap/ru5IxY0avm4UgKqUzYcIEl4WueR1q1qxpbdu2DZloFEiPCKIDAAAAQDqgAMby5ctdCZfgILqyBC+88EI7ePCg102MWEuXLnUBW395l8OHDwcmSXz00Ue9bl7Eql+/vt1yyy3Wo0ePkO/M3LlzrVWrVi7rFimrdevW7rui74guPOmik74nNWrU4MITAE8RRAcAAACAdJKJPmTIEFebNjggOGLECFeuYsGCBV43EWb277//2uuvv+6Oi7I4E5qkDykjZ86c9vvvv7s5A4K/M+vWrbNKlSq5EQTwhi4I+ku6BI/mUFBdIzo0rwC8sWLFCvf7SyM3pHLlytatWzf3nQHSs0xeNwAAAAAAcPaUTXv//fe7YJNypZRN++GHH7rA+qhRo7xuXsTSRIj+YKBuK1eudPXRNTmiMmzhnTx58timTZtcED3YwoULrXjx4p61C+YCsrqprIt/NMf48eNt0KBB1rNnT1dSBCnv008/daMFVAtdIzlk9uzZVq1aNVfi5aabbvK6iUCyIRMdAAAAANKJDz74wPr37+8mSZRixYrZgAED3MSWSFn33XefC5orazNTpkxuQkRl0CpwrokSs2bN6nUTI55K6cyZM8cmTpxo559/vhutsWXLFmvXrp279evXz+smRjQdC//FJ12I0gWo6OhodwGKiZK9Ub58eVf/fODAgSHL9V15//33A397gPSIIDoAAAAApDMHDhxwpUIKFSrkfl60aJEL3CLlKEtTAXPdVP88e/bsXjcJ8Rw5csSN3nj33XddWR1d7ND/bdq0cSWQdB8p6+OPPw4EznUBSqM2VLrF/13S7zEF0uEN/R7ThKLnnXdeyHLNvVG9enX39wZIrwiiAwAAAEA6pjrPNWvWpPZ2Kte8eXNXdqdo0aJeNyXibNy40dVG14UnTWBZoUIFr5sUsbJkyeJKhQRfgNKkyUgdmjVr5ibj7dixY8hyXXRSOZdvv/3Ws7YByY3LqgAAAAAAeGz69Ol28OBBr5sRkUqWLOlufsq0VSBXmepIWbt27bIcOXIkef1nn33Wunbt6urbI/m1aNHCnnjiCfvtt99cWR1/TXSVRFLpsMmTJ4esC6QnZKIDAAAAQDpGJnrakCtXLnesypUr53VTIh7fmbQjJibGlavie5MyMmTIkKT1oqKi+P4g3SETHQAAAAAAAGkOeaEpKy4uzusmAJ4hiA4AAAAAaVjw8PmErF27NsXaAgBIf2bNmmU7duyw6667LrBs3Lhx1q9fP9u/f7+1bNnSRowYwaSvSNcIogMAAABAGqbgRVKG1gM4ITY2NtHH9+7dm2JtAdKCgQMH2pVXXhkIomsi3rvvvts6dOhglStXtqFDh1qxYsWsf//+XjcVSDYE0QEAAAAgDWN4PXB6NAllYheWVCKEC0/Af1R3/umnnw7cnzBhgtWtW9fefvttd18T8yornSA60jOC6AAAAAAQQZo3b26jRo2yokWLet0UBOnVq5fly5fP62ZEhB9//NHrJgBpyq5du6xw4cKB+z///LM1bdo0cL9OnTq2ceNGj1oHpAyC6AAAAAAQQaZPn24HDx70uhkRXac+WIsWLdz/PXv2TMYWIViDBg1Oa/1nn33Wunbt6jLYkbpcfvnlli1bNq+bke4pgK75NZRxfuTIEVuwYIENGDAgpARS5syZPW0jkNwIogMAAAAAkMJ16kUlQ44fP57s7cHZGTx4sN16660E0T2uVR8sJibG/f+///0vGVsEv2bNmtmTTz5pzz33nH3++eeWPXt2dwHDb8mSJVa+fHlP2wgkN4LoAAAAAACcQ9SpT19UIx3e16oPrlfPxaeUpXrorVq1cqM4cubMaWPHjrUsWbIEHh89erRde+21nrYRSG4E0QEAAAAAAOApatWnXgUKFHClwPbs2eOC6BkzZgx5fOLEiW45kJ4RRAcAAAAAIBnt37/fTcS3YcMGV0842IMPPuhZu4C0XKseKS937twJLmdSZEQCgugAAAAAACSThQsXunrCBw4ccMF0BZu2b9/uagoXKlSIIDqQCH1vErr4dOGFF3rWJgCRiSA6AAAAAESQXr16kTWYgh5++GG7/vrrbeTIkS6Lc/bs2ZY5c2a744477KGHHvK6eUCqtG3bNuvYsaN98803CT5OTXQAKY0gOgAAAACkUZMnT07yui1atHD/9+zZMxlbhPgWLVpkb775pmXIkMHVET58+LCVK1fOnn/+eWvfvr2brA+p2+WXX27ZsmXzuhkRpXv37rZ7926bM2eOXXnllTZp0iTbsmWLDRo0yIYNG+Z18wBEIILoAAAAAJBGtWzZMknrRUVFkbnpEWWdK4AuKt+i0hSVK1d2WekbN270unkRJzY2NsnrxsTEuP//97//JWOLkJAffvjBvvjiC6tdu7b7/pQuXdquueYad0yGDBlizZs397qJACIMQXQAAAAASKPi4uK8bgJOoUaNGjZv3jyrUKGCmzixb9++rib6e++9ZxdccIHXzYs4efLkcReVEuPz+bjw5DHNH6CLTpI3b15X3uX888+3atWq2YIFC7xuHoAIRBAdAAAAAIBkMnjwYNu7d6/7+ZlnnrF27drZvffe64Lqo0eP9rp5EefHH3/0uglIgooVK9qKFSusTJkyVr16dVcSST9rboGiRYt63TwAESjKp0usAAAAAIB0kb35888/u5IhR44cCXnswQcf9KxdAHA63n//fTt27Jh16NDBfvvtN2vSpInt3LnTsmTJYu+++67ddtttXjcRQIQhiA4AAAAA6cDChQutWbNmduDAARdMz5cvnysbkj17dlcW4a+//vK6iRFt69atLrNWKlWqZAULFvS6Sfh/+s4kdOHpwgsv9KxNOPkYLV++3EqVKmUFChTwujkAItCJ2U0AAAAAAGnaww8/bNdff73t2rXLsmXLZrNnz7b169dbrVq17IUXXvC6eRFLpVzuvPNOK168uKuJrluxYsXsjjvusD179njdvIimOtvXXXed5cqVy6pWrerq1wff4J2BAwe6wLmfLgbWrFnTcuTI4R4DgJRGEB0AAAAA0oFFixbZI488YhkyZLCMGTPa4cOHrWTJkvb8889br169vG5exOrUqZPNmTPHvvrqK9u9e7e76ef58+fbPffc43XzIlr37t3d8dDx0YWnKVOm2NixY129+smTJ3vdvIg2YMAA27dv30nLFVjXYwCQ0phYFAAAAADSgcyZM7sAuqh8i8pTVK5c2XLnzm0bN270unkRSwHzb7/91i677LLAssaNG9vbb7/t6jzDOz/88IN98cUXVrt2bffdKV26tF1zzTUWExNjQ4YMsebNm3vdxIilysNRUVEnLV+8eLErVQUAKY0gOgAAAACkAyo/MW/ePJdFq5Ihffv2dTXR33vvPbvgggu8bl7Eyp8/v7uQEZ+W5c2b15M24QTNHaALTqJjofIu559/vlWrVs0WLFjgdfMiko6Dgue66VgEB9KPHz/ustO7du3qaRsBRCaC6AAAAACQDgwePNjV35ZnnnnG2rVrZ/fee68Lqo8ePdrr5kWs3r17W48ePdzFjCJFirhlmzdvtscee8z69OnjdfMiWsWKFd1kr2XKlLHq1avbm2++6X4eOXKkFS1a1OvmRaThw4e7LPS77rrLlW0JvgCVJUsWd3zq16/vaRsBRKYon347AQAAAACAZBkhsHr1alejvlSpUm6ZSu1ER0e7CxzByH5OWe+//74dO3bMOnToYL/99psrr7Nz504XrH333Xfttttu87qJEevnn3+2Sy+91DJlIvcTQOpAEB0AAAAA0pGtW7e67FqpVKmSFSxY0OsmRbTTmQSxX79+ydoWJE6TVi5fvtxd7ChQoIDXzYl4a9assTFjxrj/X375ZVd655tvvnHHp2rVql43D0CEIYgOAAAAAOmASrncd999NmHCBFc7WDJmzOiyaV977bUE63IDkWzgwIH26KOPWvbs2UOWHzx40IYOHermFYB3mehNmzZ12ejTp0+3ZcuWWbly5ezZZ5+1+fPn2yeffOJ1EwFEmBNTtwMAAAAA0rROnTrZnDlz7KuvvrLdu3e7m35WwOmee+7xunkRTcdi1KhR1rNnT1cuxF+65Z9//vG6aRbpowQ0UWVCGemnM4IA596TTz5pgwYNsqlTp7ryOn5XX321zZ4929O2AYhMFJcCAAAAgHRAAfNvv/3WLrvsssCyxo0b29tvv+1qPcMbS5YssUaNGrmRAOvWrbPOnTtbvnz57LPPPnO10ceNG+d1EyOWBuZHRUWdtHzx4sXuGME7v//+u40fP/6k5Srpsn37dk/aBCCykYkOAAAAAOlA/vz5EyzZomV58+b1pE0w69Gjh5u4ctWqVZY1a9bA8mbNmrkyFUh5+j4oSK4A+vnnn+9+9t/0fbnmmmvs1ltv9bqZES1Pnjy2adOmk5YvXLjQihcv7kmbAEQ2MtEBAAAAIB3o3bu3C9i+9957VqRIEbds8+bN9thjj1mfPn28bl7Emjdvnr355psnLVcgUMcHKW/48OEuC/2uu+5yZVuCLz6pdEiZMmWsfv36nrYx0rVu3dqeeOIJmzhxorvYERcXZzNnznQ17Nu1a+d18wBEIILoAAAAAJAOvPHGG7Z69WorVaqUu4nKhURHR9u2bdtCArmqx42Uof0fGxt70vKVK1dawYIFPWlTpGvfvr37v2zZsm7iykyZCI2kNoMHD7Zu3bq532XHjh2zKlWquAmT27Rp4y4YAkBK4y8FAAAAAKQDLVu29LoJSECLFi1s4MCB9vHHH7v7yqrVxQ1l2d50001eNy+iNWjQwNasWWNjxoxx/7/88suu5vY333zjgrdVq1b1uokRRxnnQ4cOtcmTJ9uRI0fszjvvdN8TTQBbo0YNq1ChgtdNBBChonwawwQAAAAAAM65PXv22M0332zz58+3vXv3WrFixVytZ5ULUbA2R44cXjcxYv3888/WtGlTl42u+vTLli2zcuXK2bPPPuuO1yeffOJ1EyPO008/bf3793eT8WbLls1Nlnz77bfb6NGjvW4agAhHEB0AAAAA0ondu3e7wJ+yalULXRMlqnRL4cKFmYzPY7/88ostWbLEZdTWqlXLGjZs6HWTIp4uZNxyyy1uLoFcuXLZ4sWLXRB97ty51qpVK/v777+9bmLEUaa56p7fc8897v73339vzZs3t4MHD1qGDBm8bh6ACMZvIAAAAABIBxSgPf/88+25556zF154wQXU5bPPPrOePXt63byIM2vWLPvqq68C9y+77DKXdf7666+7zNouXbrY4cOHPW1jpPv999/txhtvPGm5Srps377dkzZFOpU6atasWeC+MtJVAunff//1tF0AQBAdAAAAANIBZdN26NDBVq1aZVmzZg0sV0BKpSqQslQH/c8//wwJ2Hbu3NmuueYae/LJJ+3LL7+0IUOGeNrGSJcnTx5XWie+hQsXMnLDI5pENPj3l2TOnNmOHj3qWZsAQJhYFAAAAAD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",
      "text/plain": [
       "<Figure size 1500x1200 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:__main__:Saving model and results\n",
      "INFO:__main__:Saved trained model as 'bayesian_network_model.pkl'\n",
      "INFO:__main__:Saved inference results as 'inference_results.json'\n",
      "INFO:__main__:Saved processed data as 'processed_iris_data.csv'\n",
      "INFO:__main__:Saved model summary as 'model_summary.json'\n",
      "INFO:__main__:Bayesian Network implementation completed successfully!\n",
      "INFO:__main__:Final model accuracy: 0.8444\n",
      "INFO:__main__:All artifacts saved for future reference\n"
     ]
    }
   ],
   "source": [
    "# Installation commands for Google Colab and local Mac\n",
    "# !pip install pgmpy pandas numpy matplotlib seaborn scikit-learn\n",
    "\n",
    "import logging\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from pgmpy.models import DiscreteBayesianNetwork\n",
    "from pgmpy.factors.discrete import TabularCPD\n",
    "from pgmpy.inference import VariableElimination\n",
    "from pgmpy.estimators import MaximumLikelihoodEstimator, BayesianEstimator\n",
    "from sklearn.datasets import load_iris\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import KBinsDiscretizer\n",
    "import json\n",
    "import pickle\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "# Configure logging\n",
    "logging.basicConfig(\n",
    "    level=logging.INFO,\n",
    "    format='%(asctime)s - %(levelname)s - %(message)s',\n",
    "    handlers=[\n",
    "        logging.FileHandler('bayesian_network_training.log'),\n",
    "        logging.StreamHandler()\n",
    "    ]\n",
    ")\n",
    "logger = logging.getLogger(__name__)\n",
    "\n",
    "def load_and_prepare_data():\n",
    "    logger.info(\"Loading and preparing Iris dataset for Bayesian Network\")\n",
    "    \n",
    "    # Load Iris dataset\n",
    "    iris = load_iris()\n",
    "    df = pd.DataFrame(iris.data, columns=iris.feature_names)\n",
    "    df['species'] = iris.target\n",
    "    \n",
    "    logger.info(f\"Original dataset shape: {df.shape}\")\n",
    "    logger.info(f\"Features: {list(df.columns)}\")\n",
    "    \n",
    "    # Discretize continuous features into categories\n",
    "    discretizer = KBinsDiscretizer(n_bins=3, encode='ordinal', strategy='quantile')\n",
    "    \n",
    "    # Create meaningful feature names\n",
    "    feature_mapping = {\n",
    "        'sepal length (cm)': 'Sepal_Length',\n",
    "        'sepal width (cm)': 'Sepal_Width', \n",
    "        'petal length (cm)': 'Petal_Length',\n",
    "        'petal width (cm)': 'Petal_Width'\n",
    "    }\n",
    "    \n",
    "    df_processed = df.copy()\n",
    "    for old_name, new_name in feature_mapping.items():\n",
    "        discretized_feature = discretizer.fit_transform(df[[old_name]]).flatten()\n",
    "        df_processed[new_name] = discretized_feature.astype(int)\n",
    "        logger.info(f\"Discretized {old_name} -> {new_name}: {len(np.unique(discretized_feature))} bins\")\n",
    "    \n",
    "    # Create final dataset with meaningful names\n",
    "    final_df = df_processed[['Sepal_Length', 'Sepal_Width', 'Petal_Length', 'Petal_Width', 'species']].copy()\n",
    "    final_df.rename(columns={'species': 'Species'}, inplace=True)\n",
    "    \n",
    "    logger.info(f\"Final processed dataset shape: {final_df.shape}\")\n",
    "    logger.info(f\"Species distribution: {final_df['Species'].value_counts().to_dict()}\")\n",
    "    \n",
    "    return final_df\n",
    "\n",
    "def create_network_structure():\n",
    "    logger.info(\"Creating Bayesian Network structure\")\n",
    "    \n",
    "    # Define network structure based on botanical knowledge\n",
    "    # Species influences all physical characteristics\n",
    "    model = DiscreteBayesianNetwork([\n",
    "        ('Species', 'Sepal_Length'),\n",
    "        ('Species', 'Sepal_Width'),\n",
    "        ('Species', 'Petal_Length'),\n",
    "        ('Species', 'Petal_Width'),\n",
    "        ('Petal_Length', 'Petal_Width')  # Petal dimensions are correlated\n",
    "    ])\n",
    "    \n",
    "    logger.info(f\"Network nodes: {model.nodes()}\")\n",
    "    logger.info(f\"Network edges: {model.edges()}\")\n",
    "    logger.info(\"Network structure created successfully (DAG validation will occur after parameter learning)\")\n",
    "    \n",
    "    return model\n",
    "\n",
    "def learn_parameters(model, data):\n",
    "    logger.info(\"Learning network parameters using Maximum Likelihood Estimation\")\n",
    "    \n",
    "    # Fit the model to data\n",
    "    model.fit(data, estimator=MaximumLikelihoodEstimator)\n",
    "    \n",
    "    # Now we can check if the model is valid\n",
    "    try:\n",
    "        model.check_model()\n",
    "        logger.info(\"Model validation passed - all CPDs are properly defined\")\n",
    "    except Exception as e:\n",
    "        logger.warning(f\"Model validation warning: {e}\")\n",
    "    \n",
    "    logger.info(\"Learned Conditional Probability Distributions:\")\n",
    "    for cpd in model.get_cpds():\n",
    "        logger.info(f\"CPD for {cpd.variable}:\")\n",
    "        logger.info(f\"  Variables: {cpd.variables}\")\n",
    "        \n",
    "        # Use the correct attribute name for cardinalities\n",
    "        try:\n",
    "            if hasattr(cpd, 'cardinality'):\n",
    "                logger.info(f\"  Cardinality: {cpd.cardinality}\")\n",
    "            elif hasattr(cpd, 'get_cardinality'):\n",
    "                logger.info(f\"  Cardinality: {cpd.get_cardinality()}\")\n",
    "            else:\n",
    "                logger.info(f\"  Shape info: {cpd.values.shape}\")\n",
    "        except Exception as e:\n",
    "            logger.info(f\"  Shape info: {cpd.values.shape}\")\n",
    "        \n",
    "        logger.info(f\"  Values shape: {cpd.values.shape}\")\n",
    "        \n",
    "        # Log a sample of the probability values\n",
    "        if cpd.values.size <= 20:  # Only for small CPDs\n",
    "            logger.info(f\"  Sample values: {cpd.values.flatten()[:5]}\")\n",
    "    \n",
    "    return model\n",
    "\n",
    "def perform_inference(model, evidence_scenarios):\n",
    "    logger.info(\"Performing probabilistic inference\")\n",
    "    \n",
    "    # Create inference object\n",
    "    inference = VariableElimination(model)\n",
    "    results = {}\n",
    "    \n",
    "    for scenario_name, evidence in evidence_scenarios.items():\n",
    "        logger.info(f\"Inference scenario: {scenario_name}\")\n",
    "        logger.info(f\"Evidence: {evidence}\")\n",
    "        \n",
    "        try:\n",
    "            # Query probability of each species given evidence\n",
    "            result = inference.query(variables=['Species'], evidence=evidence)\n",
    "            \n",
    "            logger.info(f\"Results for {scenario_name}:\")\n",
    "            for i, prob in enumerate(result.values):\n",
    "                species_name = ['Setosa', 'Versicolor', 'Virginica'][i]\n",
    "                logger.info(f\"  P(Species={species_name}|Evidence) = {prob:.4f}\")\n",
    "            \n",
    "            results[scenario_name] = {\n",
    "                'evidence': evidence,\n",
    "                'probabilities': result.values.tolist(),\n",
    "                'species_names': ['Setosa', 'Versicolor', 'Virginica']\n",
    "            }\n",
    "        except Exception as e:\n",
    "            logger.error(f\"Error in inference for {scenario_name}: {e}\")\n",
    "            results[scenario_name] = {\n",
    "                'evidence': evidence,\n",
    "                'error': str(e)\n",
    "            }\n",
    "    \n",
    "    return results\n",
    "\n",
    "def visualize_network_and_results(model, inference_results, data):\n",
    "    logger.info(\"Creating visualizations\")\n",
    "    \n",
    "    # Set up the plotting style\n",
    "    plt.style.use('default')\n",
    "    fig, axes = plt.subplots(2, 2, figsize=(15, 12))\n",
    "    \n",
    "    # Plot 1: Data distribution\n",
    "    species_counts = data['Species'].value_counts().sort_index()\n",
    "    axes[0, 0].bar(species_counts.index, species_counts.values, alpha=0.7, edgecolor='black')\n",
    "    axes[0, 0].set_title('Species Distribution in Dataset')\n",
    "    axes[0, 0].set_xlabel('Species (0=Setosa, 1=Versicolor, 2=Virginica)')\n",
    "    axes[0, 0].set_ylabel('Count')\n",
    "    axes[0, 0].set_xticks([0, 1, 2])\n",
    "    \n",
    "    # Plot 2: Feature correlation heatmap\n",
    "    correlation_matrix = data.corr()\n",
    "    sns.heatmap(correlation_matrix, annot=True, cmap='coolwarm', center=0, ax=axes[0, 1], fmt='.3f')\n",
    "    axes[0, 1].set_title('Feature Correlation Matrix')\n",
    "    \n",
    "    # Plot 3: Inference results comparison\n",
    "    valid_results = {k: v for k, v in inference_results.items() if 'probabilities' in v}\n",
    "    if valid_results:\n",
    "        scenarios = list(valid_results.keys())[:3]  # Plot first 3 valid scenarios\n",
    "        species_names = ['Setosa', 'Versicolor', 'Virginica']\n",
    "        x = np.arange(len(species_names))\n",
    "        width = 0.25\n",
    "        \n",
    "        colors = ['skyblue', 'lightcoral', 'lightgreen']\n",
    "        for i, scenario in enumerate(scenarios):\n",
    "            probs = valid_results[scenario]['probabilities']\n",
    "            axes[1, 0].bar(x + i*width, probs, width, label=scenario, alpha=0.8, color=colors[i])\n",
    "        \n",
    "        axes[1, 0].set_xlabel('Species')\n",
    "        axes[1, 0].set_ylabel('Probability')\n",
    "        axes[1, 0].set_title('Inference Results Comparison')\n",
    "        axes[1, 0].set_xticks(x + width)\n",
    "        axes[1, 0].set_xticklabels(species_names)\n",
    "        axes[1, 0].legend()\n",
    "        axes[1, 0].set_ylim(0, 1)\n",
    "    else:\n",
    "        axes[1, 0].text(0.5, 0.5, 'No valid inference results', \n",
    "                       ha='center', va='center', transform=axes[1, 0].transAxes)\n",
    "        axes[1, 0].set_title('Inference Results (No Valid Results)')\n",
    "    \n",
    "    # Plot 4: Model structure visualization (simplified)\n",
    "    # Create adjacency matrix for network structure\n",
    "    nodes = list(model.nodes())\n",
    "    adj_matrix = np.zeros((len(nodes), len(nodes)))\n",
    "    node_to_idx = {node: i for i, node in enumerate(nodes)}\n",
    "    \n",
    "    for edge in model.edges():\n",
    "        i, j = node_to_idx[edge[0]], node_to_idx[edge[1]]\n",
    "        adj_matrix[i][j] = 1\n",
    "    \n",
    "    sns.heatmap(adj_matrix, annot=True, xticklabels=nodes, yticklabels=nodes, \n",
    "                cmap='Blues', ax=axes[1, 1], cbar=False, fmt='g')\n",
    "    axes[1, 1].set_title('Network Structure (Adjacency Matrix)')\n",
    "    axes[1, 1].set_xlabel('Child Nodes')\n",
    "    axes[1, 1].set_ylabel('Parent Nodes')\n",
    "    \n",
    "    plt.tight_layout()\n",
    "    plt.savefig('bayesian_network_analysis.png', dpi=300, bbox_inches='tight')\n",
    "    logger.info(\"Saved visualization as 'bayesian_network_analysis.png'\")\n",
    "    plt.show()\n",
    "\n",
    "def evaluate_model_performance(model, data):\n",
    "    logger.info(\"Evaluating model performance\")\n",
    "    \n",
    "    # Split data for evaluation\n",
    "    train_data, test_data = train_test_split(data, test_size=0.3, random_state=42, stratify=data['Species'])\n",
    "    logger.info(f\"Training data shape: {train_data.shape}\")\n",
    "    logger.info(f\"Test data shape: {test_data.shape}\")\n",
    "    \n",
    "    # Train model on training data\n",
    "    train_model = DiscreteBayesianNetwork(model.edges())\n",
    "    train_model.fit(train_data, estimator=MaximumLikelihoodEstimator)\n",
    "    \n",
    "    # Perform inference on test data\n",
    "    inference = VariableElimination(train_model)\n",
    "    correct_predictions = 0\n",
    "    total_predictions = 0\n",
    "    \n",
    "    prediction_details = []\n",
    "    \n",
    "    for idx, row in test_data.iterrows():\n",
    "        try:\n",
    "            # Use all features except Species as evidence\n",
    "            evidence = {col: int(row[col]) for col in data.columns if col != 'Species'}\n",
    "            \n",
    "            # Query for Species\n",
    "            result = inference.query(variables=['Species'], evidence=evidence)\n",
    "            predicted_species = np.argmax(result.values)\n",
    "            actual_species = int(row['Species'])\n",
    "            \n",
    "            prediction_details.append({\n",
    "                'actual': actual_species,\n",
    "                'predicted': predicted_species,\n",
    "                'confidence': float(np.max(result.values)),\n",
    "                'evidence': evidence\n",
    "            })\n",
    "            \n",
    "            if predicted_species == actual_species:\n",
    "                correct_predictions += 1\n",
    "            total_predictions += 1\n",
    "        except Exception as e:\n",
    "            logger.warning(f\"Could not make prediction for row {idx}: {e}\")\n",
    "    \n",
    "    if total_predictions > 0:\n",
    "        accuracy = correct_predictions / total_predictions\n",
    "        logger.info(f\"Model accuracy on test data: {accuracy:.4f} ({correct_predictions}/{total_predictions})\")\n",
    "        \n",
    "        # Log some prediction examples\n",
    "        logger.info(\"Sample predictions:\")\n",
    "        for i, pred in enumerate(prediction_details[:5]):\n",
    "            result = \"✓\" if pred['actual'] == pred['predicted'] else \"✗\"\n",
    "            logger.info(f\"  {result} Actual: {pred['actual']}, Predicted: {pred['predicted']}, Confidence: {pred['confidence']:.3f}\")\n",
    "    else:\n",
    "        accuracy = 0.0\n",
    "        logger.warning(\"No successful predictions made\")\n",
    "    \n",
    "    return accuracy, train_model\n",
    "\n",
    "def save_model_and_results(model, inference_results, accuracy, data):\n",
    "    logger.info(\"Saving model and results\")\n",
    "    \n",
    "    # Save the trained model\n",
    "    with open('bayesian_network_model.pkl', 'wb') as f:\n",
    "        pickle.dump(model, f)\n",
    "    logger.info(\"Saved trained model as 'bayesian_network_model.pkl'\")\n",
    "    \n",
    "    # Save inference results\n",
    "    with open('inference_results.json', 'w') as f:\n",
    "        json.dump(inference_results, f, indent=2)\n",
    "    logger.info(\"Saved inference results as 'inference_results.json'\")\n",
    "    \n",
    "    # Save processed data\n",
    "    data.to_csv('processed_iris_data.csv', index=False)\n",
    "    logger.info(\"Saved processed data as 'processed_iris_data.csv'\")\n",
    "    \n",
    "    # Save model summary\n",
    "    summary = {\n",
    "        'model_type': 'Discrete Bayesian Network',\n",
    "        'dataset': 'Iris (discretized)',\n",
    "        'nodes': list(model.nodes()),\n",
    "        'edges': list(model.edges()),\n",
    "        'accuracy': accuracy,\n",
    "        'data_shape': list(data.shape),\n",
    "        'num_parameters': sum(cpd.values.size for cpd in model.get_cpds()),\n",
    "        'inference_scenarios': len(inference_results)\n",
    "    }\n",
    "    \n",
    "    with open('model_summary.json', 'w') as f:\n",
    "        json.dump(summary, f, indent=2)\n",
    "    logger.info(\"Saved model summary as 'model_summary.json'\")\n",
    "\n",
    "def main():\n",
    "    logger.info(\"Starting Bayesian Network implementation\")\n",
    "    \n",
    "    # Load and prepare data\n",
    "    data = load_and_prepare_data()\n",
    "    \n",
    "    # Create network structure\n",
    "    model = create_network_structure()\n",
    "    \n",
    "    # Learn parameters\n",
    "    trained_model = learn_parameters(model, data)\n",
    "    \n",
    "    # Define inference scenarios\n",
    "    evidence_scenarios = {\n",
    "        'large_petals': {'Petal_Length': 2, 'Petal_Width': 2},  # Large petals\n",
    "        'small_petals': {'Petal_Length': 0, 'Petal_Width': 0},  # Small petals\n",
    "        'medium_sepals': {'Sepal_Length': 1, 'Sepal_Width': 1}, # Medium sepals\n",
    "        'mixed_features': {'Sepal_Length': 2, 'Petal_Length': 0} # Mixed evidence\n",
    "    }\n",
    "    \n",
    "    # Perform inference\n",
    "    inference_results = perform_inference(trained_model, evidence_scenarios)\n",
    "    \n",
    "    # Evaluate model\n",
    "    accuracy, _ = evaluate_model_performance(trained_model, data)\n",
    "    \n",
    "    # Create visualizations\n",
    "    visualize_network_and_results(trained_model, inference_results, data)\n",
    "    \n",
    "    # Save everything\n",
    "    save_model_and_results(trained_model, inference_results, accuracy, data)\n",
    "    \n",
    "    logger.info(\"Bayesian Network implementation completed successfully!\")\n",
    "    logger.info(f\"Final model accuracy: {accuracy:.4f}\")\n",
    "    logger.info(\"All artifacts saved for future reference\")\n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "    main()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9b1c9a62-2365-4b37-8cdd-f58fa091f63d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Bayesian Networks Implementation - Fully Commented Version\n",
    "# This implementation demonstrates probabilistic graphical models for classification\n",
    "# using the Iris dataset with discrete features\n",
    "\n",
    "# Installation commands for dependency management\n",
    "# Google Colab: !pip install pgmpy pandas numpy matplotlib seaborn scikit-learn\n",
    "# Local Mac: pip install pgmpy pandas numpy matplotlib seaborn scikit-learn\n",
    "\n",
    "import logging\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from pgmpy.models import DiscreteBayesianNetwork  # Updated from deprecated BayesianNetwork\n",
    "from pgmpy.factors.discrete import TabularCPD\n",
    "from pgmpy.inference import VariableElimination  # For probabilistic queries\n",
    "from pgmpy.estimators import MaximumLikelihoodEstimator, BayesianEstimator\n",
    "from sklearn.datasets import load_iris\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import KBinsDiscretizer  # Convert continuous to discrete\n",
    "import json\n",
    "import pickle\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')  # Suppress non-critical warnings\n",
    "\n",
    "# Configure comprehensive logging system\n",
    "# This captures all major steps for debugging and analysis\n",
    "logging.basicConfig(\n",
    "    level=logging.INFO,\n",
    "    format='%(asctime)s - %(levelname)s - %(message)s',\n",
    "    handlers=[\n",
    "        logging.FileHandler('bayesian_network_training.log'),  # Save to file\n",
    "        logging.StreamHandler()  # Display in console\n",
    "    ]\n",
    ")\n",
    "logger = logging.getLogger(__name__)\n",
    "\n",
    "def load_and_prepare_data():\n",
    "    \"\"\"\n",
    "    Load Iris dataset and convert continuous features to discrete bins.\n",
    "    \n",
    "    Bayesian Networks require discrete variables, so we discretize continuous\n",
    "    features into 3 bins using quantile-based binning for balanced distribution.\n",
    "    \n",
    "    Returns:\n",
    "        pd.DataFrame: Processed dataset with discrete features\n",
    "    \"\"\"\n",
    "    logger.info(\"Loading and preparing Iris dataset for Bayesian Network\")\n",
    "    \n",
    "    # Load the classic Iris dataset (150 samples, 4 features, 3 species)\n",
    "    iris = load_iris()\n",
    "    df = pd.DataFrame(iris.data, columns=iris.feature_names)\n",
    "    df['species'] = iris.target\n",
    "    \n",
    "    logger.info(f\"Original dataset shape: {df.shape}\")\n",
    "    logger.info(f\"Features: {list(df.columns)}\")\n",
    "    \n",
    "    # Discretize continuous features into 3 bins (small, medium, large)\n",
    "    # Strategy='quantile' ensures each bin has approximately equal samples\n",
    "    discretizer = KBinsDiscretizer(n_bins=3, encode='ordinal', strategy='quantile')\n",
    "    \n",
    "    # Create meaningful, shorter feature names for network clarity\n",
    "    feature_mapping = {\n",
    "        'sepal length (cm)': 'Sepal_Length',\n",
    "        'sepal width (cm)': 'Sepal_Width', \n",
    "        'petal length (cm)': 'Petal_Length',\n",
    "        'petal width (cm)': 'Petal_Width'\n",
    "    }\n",
    "    \n",
    "    df_processed = df.copy()\n",
    "    \n",
    "    # Transform each continuous feature to discrete bins (0, 1, 2)\n",
    "    for old_name, new_name in feature_mapping.items():\n",
    "        # Fit discretizer and transform data\n",
    "        discretized_feature = discretizer.fit_transform(df[[old_name]]).flatten()\n",
    "        # Convert to integers for cleaner representation\n",
    "        df_processed[new_name] = discretized_feature.astype(int)\n",
    "        logger.info(f\"Discretized {old_name} -> {new_name}: {len(np.unique(discretized_feature))} bins\")\n",
    "    \n",
    "    # Create final dataset with only the processed features we need\n",
    "    final_df = df_processed[['Sepal_Length', 'Sepal_Width', 'Petal_Length', 'Petal_Width', 'species']].copy()\n",
    "    final_df.rename(columns={'species': 'Species'}, inplace=True)\n",
    "    \n",
    "    logger.info(f\"Final processed dataset shape: {final_df.shape}\")\n",
    "    logger.info(f\"Species distribution: {final_df['Species'].value_counts().to_dict()}\")\n",
    "    \n",
    "    return final_df\n",
    "\n",
    "def create_network_structure():\n",
    "    \"\"\"\n",
    "    Define the Bayesian Network structure based on botanical domain knowledge.\n",
    "    \n",
    "    Network Design Rationale:\n",
    "    - Species is the root cause (influences all physical characteristics)\n",
    "    - All morphological features depend on species\n",
    "    - Petal dimensions are correlated (petal length influences petal width)\n",
    "    \n",
    "    This creates a DAG (Directed Acyclic Graph) representing causal relationships.\n",
    "    \n",
    "    Returns:\n",
    "        DiscreteBayesianNetwork: Network structure without learned parameters\n",
    "    \"\"\"\n",
    "    logger.info(\"Creating Bayesian Network structure\")\n",
    "    \n",
    "    # Define edges representing causal relationships\n",
    "    # Format: (parent, child) - parent causes/influences child\n",
    "    model = DiscreteBayesianNetwork([\n",
    "        ('Species', 'Sepal_Length'),      # Species determines sepal length\n",
    "        ('Species', 'Sepal_Width'),       # Species determines sepal width\n",
    "        ('Species', 'Petal_Length'),      # Species determines petal length\n",
    "        ('Species', 'Petal_Width'),       # Species determines petal width\n",
    "        ('Petal_Length', 'Petal_Width')   # Petal dimensions are correlated\n",
    "    ])\n",
    "    \n",
    "    # Log network structure for verification\n",
    "    logger.info(f\"Network nodes: {model.nodes()}\")\n",
    "    logger.info(f\"Network edges: {model.edges()}\")\n",
    "    logger.info(\"Network structure created successfully (DAG validation will occur after parameter learning)\")\n",
    "    \n",
    "    return model\n",
    "\n",
    "def learn_parameters(model, data):\n",
    "    \"\"\"\n",
    "    Learn Conditional Probability Distributions (CPDs) from data using MLE.\n",
    "    \n",
    "    Maximum Likelihood Estimation finds parameter values that maximize\n",
    "    the likelihood of observing the training data.\n",
    "    \n",
    "    Args:\n",
    "        model: Network structure\n",
    "        data: Training data\n",
    "    \n",
    "    Returns:\n",
    "        DiscreteBayesianNetwork: Trained model with learned CPDs\n",
    "    \"\"\"\n",
    "    logger.info(\"Learning network parameters using Maximum Likelihood Estimation\")\n",
    "    \n",
    "    # Fit model parameters to data using Maximum Likelihood Estimation\n",
    "    # This automatically creates CPDs for each node based on observed frequencies\n",
    "    model.fit(data, estimator=MaximumLikelihoodEstimator)\n",
    "    \n",
    "    # Validate that the model is properly constructed\n",
    "    try:\n",
    "        model.check_model()  # Verifies all CPDs are valid and consistent\n",
    "        logger.info(\"Model validation passed - all CPDs are properly defined\")\n",
    "    except Exception as e:\n",
    "        logger.warning(f\"Model validation warning: {e}\")\n",
    "    \n",
    "    # Log details about learned probability distributions\n",
    "    logger.info(\"Learned Conditional Probability Distributions:\")\n",
    "    for cpd in model.get_cpds():\n",
    "        logger.info(f\"CPD for {cpd.variable}:\")\n",
    "        logger.info(f\"  Variables: {cpd.variables}\")  # Shows variable and its parents\n",
    "        \n",
    "        # Safely access cardinality information (number of states per variable)\n",
    "        try:\n",
    "            if hasattr(cpd, 'cardinality'):\n",
    "                logger.info(f\"  Cardinality: {cpd.cardinality}\")\n",
    "            elif hasattr(cpd, 'get_cardinality'):\n",
    "                logger.info(f\"  Cardinality: {cpd.get_cardinality()}\")\n",
    "            else:\n",
    "                logger.info(f\"  Shape info: {cpd.values.shape}\")\n",
    "        except Exception as e:\n",
    "            logger.info(f\"  Shape info: {cpd.values.shape}\")\n",
    "        \n",
    "        logger.info(f\"  Values shape: {cpd.values.shape}\")\n",
    "        \n",
    "        # Show sample probability values for smaller CPDs\n",
    "        if cpd.values.size <= 20:  # Only for manageable sizes\n",
    "            logger.info(f\"  Sample values: {cpd.values.flatten()[:5]}\")\n",
    "    \n",
    "    return model\n",
    "\n",
    "def perform_inference(model, evidence_scenarios):\n",
    "    \"\"\"\n",
    "    Perform probabilistic inference for different evidence scenarios.\n",
    "    \n",
    "    Uses Variable Elimination algorithm for exact inference to compute\n",
    "    P(Species | Evidence) for various combinations of observed features.\n",
    "    \n",
    "    Args:\n",
    "        model: Trained Bayesian Network\n",
    "        evidence_scenarios: Dict of scenario_name -> evidence_dict\n",
    "    \n",
    "    Returns:\n",
    "        dict: Results for each inference scenario\n",
    "    \"\"\"\n",
    "    logger.info(\"Performing probabilistic inference\")\n",
    "    \n",
    "    # Create inference engine using Variable Elimination (exact inference)\n",
    "    inference = VariableElimination(model)\n",
    "    results = {}\n",
    "    \n",
    "    # Process each evidence scenario\n",
    "    for scenario_name, evidence in evidence_scenarios.items():\n",
    "        logger.info(f\"Inference scenario: {scenario_name}\")\n",
    "        logger.info(f\"Evidence: {evidence}\")\n",
    "        \n",
    "        try:\n",
    "            # Query: Given evidence, what's the probability distribution over Species?\n",
    "            result = inference.query(variables=['Species'], evidence=evidence)\n",
    "            \n",
    "            # Log human-readable results\n",
    "            logger.info(f\"Results for {scenario_name}:\")\n",
    "            species_names = ['Setosa', 'Versicolor', 'Virginica']\n",
    "            for i, prob in enumerate(result.values):\n",
    "                logger.info(f\"  P(Species={species_names[i]}|Evidence) = {prob:.4f}\")\n",
    "            \n",
    "            # Store results for later analysis and visualization\n",
    "            results[scenario_name] = {\n",
    "                'evidence': evidence,\n",
    "                'probabilities': result.values.tolist(),\n",
    "                'species_names': species_names\n",
    "            }\n",
    "        except Exception as e:\n",
    "            # Handle cases where evidence is impossible/inconsistent\n",
    "            logger.error(f\"Error in inference for {scenario_name}: {e}\")\n",
    "            results[scenario_name] = {\n",
    "                'evidence': evidence,\n",
    "                'error': str(e)\n",
    "            }\n",
    "    \n",
    "    return results\n",
    "\n",
    "def visualize_network_and_results(model, inference_results, data):\n",
    "    \"\"\"\n",
    "    Create comprehensive visualizations of the network and inference results.\n",
    "    \n",
    "    Generates 4 subplots:\n",
    "    1. Species distribution in dataset\n",
    "    2. Feature correlation heatmap\n",
    "    3. Inference results comparison\n",
    "    4. Network structure adjacency matrix\n",
    "    \n",
    "    Args:\n",
    "        model: Trained network\n",
    "        inference_results: Results from inference scenarios\n",
    "        data: Original dataset\n",
    "    \"\"\"\n",
    "    logger.info(\"Creating visualizations\")\n",
    "    \n",
    "    # Set up matplotlib style and create subplot grid\n",
    "    plt.style.use('default')\n",
    "    fig, axes = plt.subplots(2, 2, figsize=(15, 12))\n",
    "    \n",
    "    # Plot 1: Species distribution (shows balanced dataset)\n",
    "    species_counts = data['Species'].value_counts().sort_index()\n",
    "    axes[0, 0].bar(species_counts.index, species_counts.values, alpha=0.7, edgecolor='black')\n",
    "    axes[0, 0].set_title('Species Distribution in Dataset')\n",
    "    axes[0, 0].set_xlabel('Species (0=Setosa, 1=Versicolor, 2=Virginica)')\n",
    "    axes[0, 0].set_ylabel('Count')\n",
    "    axes[0, 0].set_xticks([0, 1, 2])\n",
    "    \n",
    "    # Plot 2: Feature correlation matrix (shows relationships between features)\n",
    "    correlation_matrix = data.corr()\n",
    "    sns.heatmap(correlation_matrix, annot=True, cmap='coolwarm', center=0, ax=axes[0, 1], fmt='.3f')\n",
    "    axes[0, 1].set_title('Feature Correlation Matrix')\n",
    "    \n",
    "    # Plot 3: Inference results comparison (shows model predictions)\n",
    "    valid_results = {k: v for k, v in inference_results.items() if 'probabilities' in v}\n",
    "    if valid_results:\n",
    "        scenarios = list(valid_results.keys())[:3]  # Show first 3 valid scenarios\n",
    "        species_names = ['Setosa', 'Versicolor', 'Virginica']\n",
    "        x = np.arange(len(species_names))  # Species positions\n",
    "        width = 0.25  # Bar width for grouped bars\n",
    "        \n",
    "        # Use distinct colors for each scenario\n",
    "        colors = ['skyblue', 'lightcoral', 'lightgreen']\n",
    "        for i, scenario in enumerate(scenarios):\n",
    "            probs = valid_results[scenario]['probabilities']\n",
    "            # Offset bars for each scenario to create grouped bar chart\n",
    "            axes[1, 0].bar(x + i*width, probs, width, label=scenario, alpha=0.8, color=colors[i])\n",
    "        \n",
    "        axes[1, 0].set_xlabel('Species')\n",
    "        axes[1, 0].set_ylabel('Probability')\n",
    "        axes[1, 0].set_title('Inference Results Comparison')\n",
    "        axes[1, 0].set_xticks(x + width)  # Center ticks between grouped bars\n",
    "        axes[1, 0].set_xticklabels(species_names)\n",
    "        axes[1, 0].legend()\n",
    "        axes[1, 0].set_ylim(0, 1)  # Probability range [0, 1]\n",
    "    else:\n",
    "        # Handle case where no valid inference results exist\n",
    "        axes[1, 0].text(0.5, 0.5, 'No valid inference results', \n",
    "                       ha='center', va='center', transform=axes[1, 0].transAxes)\n",
    "        axes[1, 0].set_title('Inference Results (No Valid Results)')\n",
    "    \n",
    "    # Plot 4: Network structure as adjacency matrix\n",
    "    nodes = list(model.nodes())\n",
    "    adj_matrix = np.zeros((len(nodes), len(nodes)))  # Initialize empty matrix\n",
    "    node_to_idx = {node: i for i, node in enumerate(nodes)}  # Map node names to indices\n",
    "    \n",
    "    # Fill adjacency matrix: 1 if edge exists, 0 otherwise\n",
    "    for edge in model.edges():\n",
    "        parent_idx, child_idx = node_to_idx[edge[0]], node_to_idx[edge[1]]\n",
    "        adj_matrix[parent_idx][child_idx] = 1\n",
    "    \n",
    "    # Create heatmap of network structure\n",
    "    sns.heatmap(adj_matrix, annot=True, xticklabels=nodes, yticklabels=nodes, \n",
    "                cmap='Blues', ax=axes[1, 1], cbar=False, fmt='g')\n",
    "    axes[1, 1].set_title('Network Structure (Adjacency Matrix)')\n",
    "    axes[1, 1].set_xlabel('Child Nodes')\n",
    "    axes[1, 1].set_ylabel('Parent Nodes')\n",
    "    \n",
    "    # Save and display the complete visualization\n",
    "    plt.tight_layout()\n",
    "    plt.savefig('bayesian_network_analysis.png', dpi=300, bbox_inches='tight')\n",
    "    logger.info(\"Saved visualization as 'bayesian_network_analysis.png'\")\n",
    "    plt.show()\n",
    "\n",
    "def evaluate_model_performance(model, data):\n",
    "    \"\"\"\n",
    "    Evaluate model performance using train/test split with stratification.\n",
    "    \n",
    "    Performance Evaluation Strategy:\n",
    "    - Stratified split maintains class balance in train/test sets\n",
    "    - Use all features except Species as evidence for prediction\n",
    "    - Predict Species and compare with ground truth\n",
    "    - Calculate accuracy and log sample predictions with confidence\n",
    "    \n",
    "    Args:\n",
    "        model: Trained Bayesian Network\n",
    "        data: Complete dataset\n",
    "    \n",
    "    Returns:\n",
    "        tuple: (accuracy_score, trained_model_on_train_split)\n",
    "    \"\"\"\n",
    "    logger.info(\"Evaluating model performance\")\n",
    "    \n",
    "    # Create stratified train/test split (maintains class distribution)\n",
    "    # test_size=0.3 means 30% for testing, 70% for training\n",
    "    # stratify ensures equal representation of each species in both sets\n",
    "    train_data, test_data = train_test_split(data, test_size=0.3, random_state=42, stratify=data['Species'])\n",
    "    logger.info(f\"Training data shape: {train_data.shape}\")\n",
    "    logger.info(f\"Test data shape: {test_data.shape}\")\n",
    "    \n",
    "    # Train a new model on training data only (proper evaluation)\n",
    "    train_model = DiscreteBayesianNetwork(model.edges())  # Same structure\n",
    "    train_model.fit(train_data, estimator=MaximumLikelihoodEstimator)\n",
    "    \n",
    "    # Create inference engine for the trained model\n",
    "    inference = VariableElimination(train_model)\n",
    "    correct_predictions = 0\n",
    "    total_predictions = 0\n",
    "    \n",
    "    prediction_details = []  # Store details for analysis\n",
    "    \n",
    "    # Evaluate on each test sample\n",
    "    for idx, row in test_data.iterrows():\n",
    "        try:\n",
    "            # Create evidence dictionary (all features except target Species)\n",
    "            evidence = {col: int(row[col]) for col in data.columns if col != 'Species'}\n",
    "            \n",
    "            # Perform inference: P(Species | evidence)\n",
    "            result = inference.query(variables=['Species'], evidence=evidence)\n",
    "            \n",
    "            # Make prediction (species with highest probability)\n",
    "            predicted_species = np.argmax(result.values)\n",
    "            actual_species = int(row['Species'])\n",
    "            \n",
    "            # Store prediction details for analysis\n",
    "            prediction_details.append({\n",
    "                'actual': actual_species,\n",
    "                'predicted': predicted_species,\n",
    "                'confidence': float(np.max(result.values)),  # Highest probability\n",
    "                'evidence': evidence\n",
    "            })\n",
    "            \n",
    "            # Count correct predictions\n",
    "            if predicted_species == actual_species:\n",
    "                correct_predictions += 1\n",
    "            total_predictions += 1\n",
    "            \n",
    "        except Exception as e:\n",
    "            # Log failed predictions (e.g., due to unseen evidence combinations)\n",
    "            logger.warning(f\"Could not make prediction for row {idx}: {e}\")\n",
    "    \n",
    "    # Calculate and report accuracy\n",
    "    if total_predictions > 0:\n",
    "        accuracy = correct_predictions / total_predictions\n",
    "        logger.info(f\"Model accuracy on test data: {accuracy:.4f} ({correct_predictions}/{total_predictions})\")\n",
    "        \n",
    "        # Show sample predictions with confidence scores\n",
    "        logger.info(\"Sample predictions:\")\n",
    "        for i, pred in enumerate(prediction_details[:5]):  # Show first 5 predictions\n",
    "            result_symbol = \"✓\" if pred['actual'] == pred['predicted'] else \"✗\"\n",
    "            logger.info(f\"  {result_symbol} Actual: {pred['actual']}, Predicted: {pred['predicted']}, Confidence: {pred['confidence']:.3f}\")\n",
    "    else:\n",
    "        accuracy = 0.0\n",
    "        logger.warning(\"No successful predictions made\")\n",
    "    \n",
    "    return accuracy, train_model\n",
    "\n",
    "def save_model_and_results(model, inference_results, accuracy, data):\n",
    "    \"\"\"\n",
    "    Save all important artifacts for reproducibility and future use.\n",
    "    \n",
    "    Saves:\n",
    "    - Trained model (pickle format for Python)\n",
    "    - Inference results (JSON for cross-platform compatibility)\n",
    "    - Processed data (CSV for analysis in other tools)\n",
    "    - Model summary (JSON with metadata)\n",
    "    \n",
    "    Args:\n",
    "        model: Trained Bayesian Network\n",
    "        inference_results: Dictionary of inference scenarios and results\n",
    "        accuracy: Model accuracy score\n",
    "        data: Processed dataset\n",
    "    \"\"\"\n",
    "    logger.info(\"Saving model and results\")\n",
    "    \n",
    "    # Save trained model using pickle (preserves Python objects)\n",
    "    with open('bayesian_network_model.pkl', 'wb') as f:\n",
    "        pickle.dump(model, f)\n",
    "    logger.info(\"Saved trained model as 'bayesian_network_model.pkl'\")\n",
    "    \n",
    "    # Save inference results as JSON (human-readable, cross-platform)\n",
    "    with open('inference_results.json', 'w') as f:\n",
    "        json.dump(inference_results, f, indent=2)\n",
    "    logger.info(\"Saved inference results as 'inference_results.json'\")\n",
    "    \n",
    "    # Save processed data as CSV (can be opened in Excel, loaded by other tools)\n",
    "    data.to_csv('processed_iris_data.csv', index=False)\n",
    "    logger.info(\"Saved processed data as 'processed_iris_data.csv'\")\n",
    "    \n",
    "    # Create comprehensive model summary\n",
    "    summary = {\n",
    "        'model_type': 'Discrete Bayesian Network',\n",
    "        'dataset': 'Iris (discretized)',\n",
    "        'nodes': list(model.nodes()),\n",
    "        'edges': list(model.edges()),\n",
    "        'accuracy': accuracy,\n",
    "        'data_shape': list(data.shape),\n",
    "        'num_parameters': sum(cpd.values.size for cpd in model.get_cpds()),  # Total parameters\n",
    "        'inference_scenarios': len(inference_results)\n",
    "    }\n",
    "    \n",
    "    # Save model summary as JSON\n",
    "    with open('model_summary.json', 'w') as f:\n",
    "        json.dump(summary, f, indent=2)\n",
    "    logger.info(\"Saved model summary as 'model_summary.json'\")\n",
    "\n",
    "def main():\n",
    "    \"\"\"\n",
    "    Main execution function that orchestrates the complete Bayesian Network workflow.\n",
    "    \n",
    "    Workflow:\n",
    "    1. Data loading and preprocessing\n",
    "    2. Network structure definition\n",
    "    3. Parameter learning from data\n",
    "    4. Probabilistic inference with test scenarios\n",
    "    5. Model evaluation and performance measurement\n",
    "    6. Visualization and results analysis\n",
    "    7. Artifact saving for reproducibility\n",
    "    \"\"\"\n",
    "    logger.info(\"Starting Bayesian Network implementation\")\n",
    "    \n",
    "    # Step 1: Load and preprocess data\n",
    "    data = load_and_prepare_data()\n",
    "    \n",
    "    # Step 2: Define network structure based on domain knowledge\n",
    "    model = create_network_structure()\n",
    "    \n",
    "    # Step 3: Learn parameters (CPDs) from data using MLE\n",
    "    trained_model = learn_parameters(model, data)\n",
    "    \n",
    "    # Step 4: Define test scenarios for inference\n",
    "    # These scenarios test different combinations of evidence\n",
    "    evidence_scenarios = {\n",
    "        'large_petals': {'Petal_Length': 2, 'Petal_Width': 2},    # Expect Virginica\n",
    "        'small_petals': {'Petal_Length': 0, 'Petal_Width': 0},   # Expect Setosa  \n",
    "        'medium_sepals': {'Sepal_Length': 1, 'Sepal_Width': 1},  # Mixed prediction\n",
    "        'mixed_features': {'Sepal_Length': 2, 'Petal_Length': 0} # Potentially conflicting\n",
    "    }\n",
    "    \n",
    "    # Step 5: Perform probabilistic inference\n",
    "    inference_results = perform_inference(trained_model, evidence_scenarios)\n",
    "    \n",
    "    # Step 6: Evaluate model performance using proper train/test methodology\n",
    "    accuracy, _ = evaluate_model_performance(trained_model, data)\n",
    "    \n",
    "    # Step 7: Create comprehensive visualizations\n",
    "    visualize_network_and_results(trained_model, inference_results, data)\n",
    "    \n",
    "    # Step 8: Save all artifacts for future reference and reproducibility\n",
    "    save_model_and_results(trained_model, inference_results, accuracy, data)\n",
    "    \n",
    "    # Final summary\n",
    "    logger.info(\"Bayesian Network implementation completed successfully!\")\n",
    "    logger.info(f\"Final model accuracy: {accuracy:.4f}\")\n",
    "    logger.info(\"All artifacts saved for future reference\")\n",
    "\n",
    "# Entry point - execute main function when script is run directly\n",
    "if __name__ == \"__main__\":\n",
    "    main()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ea1fef14-6651-43be-800c-2e89f529aefc",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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