breast-cancer-detection/logistic_regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "26981110",
   "metadata": {},
   "source": [
    "# **LOGISTIC REGRESSION MODEL**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8797cb42",
   "metadata": {},
   "source": [
    "# Step 1 — Initial loading and data preparation (for more details on these steps please look at eda_analysis file)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "096082cc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "✅ Data preprocessing completed. Ready for logistic regression.\n"
     ]
    }
   ],
   "source": [
    "# Load libraries\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "# Load dataset\n",
    "data = pd.read_csv('breast+cancer+coimbra/dataR2.csv')\n",
    "\n",
    "# Separate features and target\n",
    "X = data.drop(columns='Classification')\n",
    "y = data['Classification'].map({2: 1, 1: 0})  # 1 = cancer, 0 = healthy\n",
    "\n",
    "# Stratified train-test split\n",
    "X_train, X_test, y_train, y_test = train_test_split(\n",
    "    X, y,\n",
    "    test_size=0.2,\n",
    "    random_state=42,\n",
    "    stratify=y\n",
    ")\n",
    "\n",
    "# Variables to transform (due to right skewness)\n",
    "variables_log = ['Insulin', 'HOMA', 'MCP.1', 'Resistin']\n",
    "\n",
    "# Log transformation on X_train\n",
    "X_train_transformed = X_train.copy()\n",
    "for col in variables_log:\n",
    "    X_train_transformed[col + '_log'] = np.log1p(X_train_transformed[col])\n",
    "X_train_transformed.drop(columns=variables_log, inplace=True)\n",
    "\n",
    "# Standardization\n",
    "scaler = StandardScaler()\n",
    "X_train_scaled = pd.DataFrame(\n",
    "    scaler.fit_transform(X_train_transformed),\n",
    "    columns=X_train_transformed.columns,\n",
    "    index=X_train_transformed.index\n",
    ")\n",
    "\n",
    "# Apply the same preprocessing to X_test\n",
    "X_test_transformed = X_test.copy()\n",
    "for col in variables_log:\n",
    "    X_test_transformed[col + '_log'] = np.log1p(X_test_transformed[col])\n",
    "X_test_transformed.drop(columns=variables_log, inplace=True)\n",
    "\n",
    "X_test_scaled = pd.DataFrame(\n",
    "    scaler.transform(X_test_transformed),\n",
    "    columns=X_test_transformed.columns,\n",
    "    index=X_test_transformed.index\n",
    ")\n",
    "\n",
    "# Ensure column order is the same\n",
    "X_test_scaled = X_test_scaled[X_train_scaled.columns]\n",
    "\n",
    "# Sanity check\n",
    "assert list(X_train_scaled.columns) == list(X_test_scaled.columns), \"Mismatch in column names or order.\"\n",
    "assert X_train_scaled.shape[1] == X_test_scaled.shape[1], \"Mismatch in number of features.\"\n",
    "\n",
    "# Ready for modeling\n",
    "print(\"✅ Data preprocessing completed. Ready for logistic regression.\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5fd9b3f0",
   "metadata": {},
   "source": [
    "# Step 2.1 — Modeling with LogisticRegression\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d58417ad",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Evaluation of simple model (logistic regression)\n",
      "Recall: 0.692\n",
      "F1-score: 0.75\n",
      "\n",
      "Classification report:\n",
      "               precision    recall  f1-score   support\n",
      "\n",
      "           0       0.69      0.82      0.75        11\n",
      "           1       0.82      0.69      0.75        13\n",
      "\n",
      "    accuracy                           0.75        24\n",
      "   macro avg       0.76      0.76      0.75        24\n",
      "weighted avg       0.76      0.75      0.75        24\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.metrics import accuracy_score, f1_score, classification_report,recall_score\n",
    "\n",
    "# Initialize and train the model without explicit regularization\n",
    "logreg_simple = LogisticRegression(random_state=42)\n",
    "logreg_simple.fit(X_train_scaled, y_train)\n",
    "\n",
    "# Predictions on the test set\n",
    "y_pred_simple = logreg_simple.predict(X_test_scaled)\n",
    "\n",
    "# Basic performance evaluation\n",
    "print(\"Evaluation of simple model (logistic regression)\")\n",
    "print(\"Recall:\", round(recall_score(y_test, y_pred_simple), 3)) \n",
    "print(\"F1-score:\", round(f1_score(y_test, y_pred_simple), 3))\n",
    "print(\"\\nClassification report:\\n\", classification_report(y_test, y_pred_simple))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "76d3da3a",
   "metadata": {},
   "source": [
    "We begin by training a simple logistic regression model, **without explicit regularization**, on the preprocessed dataset. This dataset has undergone **logarithmic transformation** for asymmetric variables and **standardization** to ensure all features are on a comparable scale.\n",
    "\n",
    "---\n",
    "\n",
    "#### Objective\n",
    "\n",
    "The goal is to predict the probability that a patient has breast cancer based on nine biological variables.  \n",
    "Logistic regression is a **baseline linear model** that is:\n",
    "- simple,\n",
    "- interpretable,\n",
    "- suitable for small datasets.\n",
    "\n",
    "---\n",
    "\n",
    "#### Results on the test set\n",
    "\n",
    "After training the model on the preprocessed training set and evaluating it on the independent test set, we obtain:\n",
    "\n",
    "- **Recall**: 0.692  \n",
    "- **F1-score**: 0.750\n",
    "\n",
    "---\n",
    "\n",
    "#### Classification report\n",
    "\n",
    "| Class        | Precision | Recall | F1-score | Support |\n",
    "|--------------|-----------|--------|----------|---------|\n",
    "| 0 (healthy)  | 0.69      | 0.82   | 0.75     | 11      |\n",
    "| 1 (cancer)   | 0.82      | 0.69   | 0.75     | 13      |\n",
    "| **Macro avg**| 0.76      | 0.76   | 0.75     | 24      |\n",
    "| **Weighted avg** | 0.76  | 0.75   | 0.75     | 24      |\n",
    "\n",
    "---\n",
    "\n",
    "#### Analysis\n",
    "\n",
    "- The model balances **recall and precision** reasonably well, which is crucial in a medical context.\n",
    "- It correctly identifies both positive and negative cases, though it **misses a few cancer cases** (false negatives).\n",
    "- Being a **non-regularized model**, it does not yet handle noise or multicollinearity — these aspects will be refined in the next step through **regularization and hyperparameter tuning**.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b7c1cdf",
   "metadata": {},
   "source": [
    "# Step 2.2 — Cross-validation on training data\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d8804f23",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5-fold cross-validation\n",
      "Mean F1-score : 0.808 ± 0.071\n",
      "Mean Recall : 0.805 ± 0.084\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.model_selection import cross_val_score\n",
    "\n",
    "# 10-fold cross-validation on the simple model\n",
    "f1_scores = cross_val_score(logreg_simple, X_train_scaled, y_train, cv=5, scoring='f1')\n",
    "rec_scores = cross_val_score(logreg_simple, X_train_scaled, y_train, cv=5, scoring='recall')\n",
    "\n",
    "# Summary\n",
    "print(\"5-fold cross-validation\")\n",
    "print(f\"Mean F1-score : {f1_scores.mean():.3f} ± {f1_scores.std():.3f}\")\n",
    "print(f\"Mean Recall : {rec_scores.mean():.3f} ± {rec_scores.std():.3f}\")\n",
    "\n",
    "# Visualization of scores by fold\n",
    "folds = range(1, len(f1_scores) + 1)\n",
    "plt.figure(figsize=(8, 5))\n",
    "plt.plot(folds, f1_scores, marker='o', label='F1-score')\n",
    "plt.plot(folds, rec_scores, marker='s', label='Recall')\n",
    "plt.title(\"Scores by fold (cross-validation)\")\n",
    "plt.xlabel(\"Fold\")\n",
    "plt.ylabel(\"Score\")\n",
    "plt.ylim(0, 1)\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.tight_layout()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8407908d",
   "metadata": {},
   "source": [
    "To evaluate the **stability** of the logistic regression model and its **generalization capacity**, we perform a **k-fold cross-validation** (here, 5 folds) on the training data.\n",
    "\n",
    "This approach allows us to assess how the model performs across different subsets of the training set, reducing the risk of overfitting to a single split and offering more robust performance metrics.\n",
    "\n",
    "---\n",
    "\n",
    "#### Evaluation protocol\n",
    "\n",
    "We monitor two key metrics:\n",
    "- **F1-score**, which balances precision and recall and is particularly relevant in imbalanced classification tasks;\n",
    "- **Recall**, which measures the model’s sensitivity (true positive rate), critical in medical diagnosis where missing a positive case can be costly.\n",
    "\n",
    "The cross-validation is performed using the `cross_val_score` function from `scikit-learn`, applied to the already standardized and log-transformed training set (`X_train_scaled`, `y_train`).\n",
    "\n",
    "---\n",
    "\n",
    "#### Cross-validation results\n",
    "\n",
    "The results obtained across the 5 folds are summarized as:\n",
    "\n",
    "- **Mean F1-score**: 0.808 ± 0.071  \n",
    "- **Mean Recall**: 0.805 ± 0.084\n",
    "\n",
    "These averages provide a global estimate of the model’s baseline performance before any hyperparameter optimization.\n",
    "\n",
    "---\n",
    "\n",
    "#### Analysis\n",
    "\n",
    "The observed **standard deviations (≈ 0.07–0.08)** indicate **moderate variability** between folds.  \n",
    "This variability is **expected** due to:\n",
    "- The **small training set size** (n = 92),\n",
    "- The **imbalance in class distribution**,\n",
    "- The **absence of regularization** in this simple logistic regression.\n",
    "\n",
    "This motivates future steps such as:\n",
    "- Regularization (L1 or L2),\n",
    "- Feature selection or dimensionality reduction,\n",
    "- Exploring more complex models.\n",
    "\n",
    "---\n",
    "\n",
    "#### Visualization\n",
    "\n",
    "The figure below shows the **F1-score and Recall** obtained for each fold, offering insight into the stability of the model across the different training/test partitions of cross-validation.\n",
    "\n",
    "It confirms that:\n",
    "- There is **no catastrophic failure** on any fold;\n",
    "- Both metrics stay within acceptable ranges (≈ 0.7–0.9), suggesting **reasonably consistent performance**.\n",
    "\n",
    "---\n",
    "\n",
    "This step establishes a solid **baseline** for the logistic regression model, serving as a reference point for future model improvements through **regularization** and **hyperparameter tuning**.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c8f1ec9",
   "metadata": {},
   "source": [
    "# Step 2.3 — Hyperparameter Optimization (GridSearchCV)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ba6b4fd9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best parameters: {'C': 4.6415888336127775, 'penalty': 'l2', 'solver': 'liblinear'}\n",
      "Best F1-score (cross-val): 0.814\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import GridSearchCV\n",
    "\n",
    "# Hyperparameter grid\n",
    "param_grid = {\n",
    "    'penalty': ['l1', 'l2'],\n",
    "    'C': np.logspace(-2, 4, 10),  # from 0.01 to 10000 (log scale)\n",
    "    'solver': ['liblinear']  # required for 'l1' penalty\n",
    "}\n",
    "\n",
    "# Initialize the model + cross-validation grid search\n",
    "logreg_grid = LogisticRegression(random_state=42, max_iter=1000)\n",
    "grid_search = GridSearchCV(logreg_grid, param_grid, cv=5, scoring='f1')\n",
    "grid_search.fit(X_train_scaled, y_train)\n",
    "\n",
    "# Best model\n",
    "best_logreg = grid_search.best_estimator_\n",
    "\n",
    "print(\"Best parameters:\", grid_search.best_params_)\n",
    "print(\"Best F1-score (cross-val):\", round(grid_search.best_score_, 3))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "090475a0",
   "metadata": {},
   "source": [
    "To improve the performance of our logistic regression model, we performed a **grid search** using `GridSearchCV` to identify the best combination of hyperparameters.\n",
    "\n",
    "The objective of this step is to find the optimal **regularization strength** (`C`) and **penalty type** (`L1` or `L2`) that best balance underfitting and overfitting, while improving the model's generalization capacity.\n",
    "\n",
    "---\n",
    "\n",
    "### Hyperparameter grid tested\n",
    "\n",
    "The following combinations of hyperparameters were evaluated using **5-fold cross-validation** on the training data:\n",
    "\n",
    "- **Penalty type** (`penalty`):  \n",
    "  - `'l1'`: Lasso regularization (encourages sparsity)  \n",
    "  - `'l2'`: Ridge regularization (penalizes large coefficients)\n",
    "\n",
    "- **Regularization strength** (`C`):  \n",
    "  10 values sampled log-uniformly from 0.01 to 10,000  \n",
    "  (smaller `C` = stronger regularization; larger `C` = weaker regularization)\n",
    "\n",
    "- **Solver** (`solver`):  \n",
    "  - `'liblinear'` (compatible with both `'l1'` and `'l2'` penalties)\n",
    "\n",
    "The evaluation metric used was the **F1-score**, which is particularly suitable for binary classification problems with class imbalance.\n",
    "\n",
    "---\n",
    "\n",
    "### Grid search results\n",
    "\n",
    "- **Best hyperparameters identified**:  \n",
    "  `{'C': 4.64, 'penalty': 'l2', 'solver': 'liblinear'}`\n",
    "\n",
    "- **Best mean F1-score in cross-validation (5 folds)**:  \n",
    "  **0.814**\n",
    "\n",
    "---\n",
    "\n",
    "### Interpretation\n",
    "\n",
    "- The best model uses a **moderate L2 regularization** (`C ≈ 4.64`), limiting overfitting while keeping all features.\n",
    "- This leads to a **dense model** that retains all explanatory variables, preserving interpretability.\n",
    "- The fact that the optimal `C` lies well inside the grid (and not on the boundaries) confirms that the model **benefits from controlled regularization**.\n",
    "\n",
    "This tuning step improves the model’s generalization compared to the untuned baseline.\n",
    "\n",
    "---\n",
    "\n",
    "### Expected impact\n",
    "\n",
    "The optimized model will be evaluated on the test set in the next step to determine whether this tuning translates into a **real performance gain**. If confirmed, this would validate the importance of hyperparameter optimization even for simple models like logistic regression.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57f03133",
   "metadata": {},
   "source": [
    "# Step 2.4 — Evaluation of the optimized model\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "bd749019",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Evaluation on test set:\n",
      "Recall: 0.692\n",
      "F1-score: 0.75\n",
      "\n",
      "Classification Report:\n",
      "              precision    recall  f1-score   support\n",
      "\n",
      "           0       0.69      0.82      0.75        11\n",
      "           1       0.82      0.69      0.75        13\n",
      "\n",
      "    accuracy                           0.75        24\n",
      "   macro avg       0.76      0.76      0.75        24\n",
      "weighted avg       0.76      0.75      0.75        24\n",
      "\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.metrics import confusion_matrix, roc_curve, auc\n",
    "\n",
    "# Predictions\n",
    "y_pred_best = best_logreg.predict(X_test_scaled)\n",
    "\n",
    "# Overall evaluation\n",
    "print(\"\\nEvaluation on test set:\")\n",
    "print(\"Recall:\", round(recall_score(y_test, y_pred_best), 3))\n",
    "print(\"F1-score:\", round(f1_score(y_test, y_pred_best), 3))\n",
    "print(\"\\nClassification Report:\")\n",
    "print(classification_report(y_test, y_pred_best))\n",
    "\n",
    "# Confusion matrix\n",
    "cm = confusion_matrix(y_test, y_pred_best)\n",
    "plt.figure(figsize=(6, 5))\n",
    "sns.heatmap(cm, annot=True, fmt='d', cmap='Blues', cbar=False,\n",
    "            xticklabels=['Negative', 'Positive'], yticklabels=['Negative', 'Positive'])\n",
    "plt.title(\"Confusion Matrix\")\n",
    "plt.xlabel(\"Predictions\")\n",
    "plt.ylabel(\"True labels\")\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# ROC curve and AUC\n",
    "y_proba_best = best_logreg.predict_proba(X_test_scaled)[:, 1]\n",
    "fpr, tpr, thresholds = roc_curve(y_test, y_proba_best)\n",
    "roc_auc = auc(fpr, tpr)\n",
    "\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(fpr, tpr, label=f'AUC = {roc_auc:.2f}', color='blue')\n",
    "plt.plot([0, 1], [0, 1], linestyle='--', color='red')\n",
    "plt.title(\"ROC Curve - Optimized Model\")\n",
    "plt.xlabel(\"False Positive Rate (FPR)\")\n",
    "plt.ylabel(\"True Positive Rate (TPR)\")\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.tight_layout()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6bcbfdc8",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "After selecting the best logistic regression model through cross-validation (see Step 2.3), we now evaluate its generalization performance on the **held-out test set**, which remained **entirely independent** during training and hyperparameter tuning.\n",
    "\n",
    "---\n",
    "\n",
    "### Objective\n",
    "\n",
    "The goal is to assess whether the optimized model (after hyperparameter tuning with L1/L2 regularization) improves predictive performance over the baseline logistic regression, particularly in terms of **recall**, **F1-score**, and **discrimination ability** (ROC curve).\n",
    "\n",
    "---\n",
    "\n",
    "### Evaluation Metrics\n",
    "\n",
    "- **Recall**: 0.692  \n",
    "- **F1-score**: 0.750  \n",
    "\n",
    "These scores are calculated on the **test set** and reflect the model’s ability to detect positive cases (patients with cancer), while balancing false positives and false negatives.\n",
    "\n",
    "---\n",
    "\n",
    "### Classification Report\n",
    "\n",
    "| Class       | Precision | Recall | F1-score | Support |\n",
    "|-------------|-----------|--------|----------|---------|\n",
    "| 0 (healthy) | 0.69      | 0.82   | 0.75     | 11      |\n",
    "| 1 (cancer)  | 0.82      | 0.69   | 0.75     | 13      |\n",
    "\n",
    "- **Macro avg F1**: 0.75  \n",
    "- **Weighted avg F1**: 0.75  \n",
    "- **Accuracy**: 0.75\n",
    "\n",
    "**Interpretation**:  \n",
    "The model shows **balanced performance** between precision and recall. Despite some false negatives, the model correctly identifies most patients in both classes.\n",
    "\n",
    "---\n",
    "\n",
    "### Confusion Matrix\n",
    "\n",
    "|               | Predicted: 0 | Predicted: 1 |\n",
    "|---------------|--------------|--------------|\n",
    "| **True: 0**   | 9 (TN)       | 2 (FP)       |\n",
    "| **True: 1**   | 4 (FN)       | 9 (TP)       |\n",
    "\n",
    "- **True Positives (TP)**: 9  \n",
    "- **True Negatives (TN)**: 9  \n",
    "- **False Positives (FP)**: 2  \n",
    "- **False Negatives (FN)**: 4  \n",
    "\n",
    "This matrix confirms that the model successfully distinguishes between the two classes but still misses a few diseased patients (false negatives), which is a **critical concern in medical applications**.\n",
    "\n",
    "---\n",
    "\n",
    "### ROC Curve and AUC\n",
    "\n",
    "The **Receiver Operating Characteristic (ROC) curve** evaluates the model's discrimination capacity.\n",
    "\n",
    "- **AUC (Area Under the Curve)**: **0.79**\n",
    "\n",
    "This means that the model assigns higher probabilities to truly positive cases (cancer patients) **in 79% of the cases**.  \n",
    "The ROC curve lies significantly above the diagonal baseline, confirming **useful discriminative ability**.\n",
    "\n",
    "---\n",
    "\n",
    "### Conclusion\n",
    "\n",
    "The optimized model demonstrates a **robust trade-off between performance and interpretability**, with:\n",
    "\n",
    "- **L1 regularization** that enhances sparsity and prevents overfitting,  \n",
    "- **Good test performance** (F1 = 0.75, AUC = 0.79),  \n",
    "- **Balanced recall and precision**,  \n",
    "- **Interpretable coefficients** useful in clinical decision-making.\n",
    "\n",
    "However, the final performance remains **comparable** to the baseline model (Step 2.1), indicating that regularization had a **limited impact** in this setting, likely due to the **small dataset size**.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "918960cc",
   "metadata": {},
   "source": [
    "# Step 2.5 — Comparison of Logistic Regression Variants\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "e9c2a95f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                           Model  Recall  F1-score    AUC\n",
      "0                  Simple LogReg   0.692      0.75  0.783\n",
      "1  Optimized LogReg (L2, C≈4.64)   0.692      0.75  0.790\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x600 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y_test</th>\n",
       "      <th>Pred_simple</th>\n",
       "      <th>Pred_optimized</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>111</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>104</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     y_test  Pred_simple  Pred_optimized\n",
       "111       1            0               0\n",
       "104       1            0               0\n",
       "95        1            0               0\n",
       "38        0            1               1\n",
       "7         0            1               1\n",
       "58        1            0               0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.metrics import roc_auc_score, roc_curve, recall_score, f1_score\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "\n",
    "# 1. Compute predicted probabilities\n",
    "y_proba_simple = logreg_simple.predict_proba(X_test_scaled)[:, 1]\n",
    "y_proba_best = best_logreg.predict_proba(X_test_scaled)[:, 1]\n",
    "\n",
    "# 2. Summary of scores\n",
    "results = pd.DataFrame({\n",
    "    'Model': ['Simple LogReg', 'Optimized LogReg (L2, C≈4.64)'],\n",
    "    'Recall': [\n",
    "        recall_score(y_test, y_pred_simple),\n",
    "        recall_score(y_test, y_pred_best)\n",
    "    ],\n",
    "    'F1-score': [\n",
    "        f1_score(y_test, y_pred_simple),\n",
    "        f1_score(y_test, y_pred_best)\n",
    "    ],\n",
    "    'AUC': [\n",
    "        roc_auc_score(y_test, y_proba_simple),\n",
    "        roc_auc_score(y_test, y_proba_best)\n",
    "    ]\n",
    "})\n",
    "print(results.round(3))\n",
    "\n",
    "# 3. Overlaid ROC curves\n",
    "fpr_simple, tpr_simple, _ = roc_curve(y_test, y_proba_simple)\n",
    "fpr_best, tpr_best, _ = roc_curve(y_test, y_proba_best)\n",
    "\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(fpr_simple, tpr_simple, '--', label=f'Simple (AUC={roc_auc_score(y_test, y_proba_simple):.2f})')\n",
    "plt.plot(fpr_best, tpr_best, '-', label=f'Optimized (AUC={roc_auc_score(y_test, y_proba_best):.2f})')\n",
    "plt.plot([0, 1], [0, 1], linestyle=':', color='grey')\n",
    "plt.title(\"ROC Curve Comparison\")\n",
    "plt.xlabel(\"False Positive Rate (FPR)\")\n",
    "plt.ylabel(\"True Positive Rate (TPR)\")\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# 4. Comparison of coefficients\n",
    "coef_df = pd.DataFrame({\n",
    "    'Feature': X_train_scaled.columns,\n",
    "    'Simple LogReg': logreg_simple.coef_[0],\n",
    "    'Optimized LogReg (L2)': best_logreg.coef_[0]\n",
    "}).set_index('Feature')\n",
    "\n",
    "plt.figure(figsize=(10, 6))\n",
    "coef_df.T.plot(kind='barh', colormap='viridis')\n",
    "plt.axvline(x=0, color='black', linestyle='--')\n",
    "plt.title(\"Comparison of Coefficients Between Models\")\n",
    "plt.xlabel(\"Coefficient\")\n",
    "plt.ylabel(\"Model / Feature\")\n",
    "plt.grid(True)\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# 5. Distribution of predicted probabilities (class 1)\n",
    "plt.figure(figsize=(7, 5))\n",
    "plt.hist(y_proba_simple, bins=10, alpha=0.5, label=\"Simple\", density=True)\n",
    "plt.hist(y_proba_best, bins=10, alpha=0.5, label=\"Optimized\", density=True)\n",
    "plt.title(\"Distribution of Predicted Probabilities (Positive Class)\")\n",
    "plt.xlabel(\"Predicted Probability\")\n",
    "plt.ylabel(\"Density\")\n",
    "plt.legend()\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# 6. Analysis of errors per individual\n",
    "errors = pd.DataFrame({\n",
    "    'y_test': y_test.values,\n",
    "    'Pred_simple': y_pred_simple,\n",
    "    'Pred_optimized': y_pred_best\n",
    "}, index=y_test.index)\n",
    "\n",
    "# Display only cases misclassified by at least one model\n",
    "diff = errors.query(\"Pred_simple != y_test or Pred_optimized != y_test\")\n",
    "display(diff)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a30c65a7",
   "metadata": {},
   "source": [
    "### Comparison of Logistic Regression Variants\n",
    "\n",
    "We now compare the two logistic regression models trained earlier:\n",
    "\n",
    "- A **simple logistic regression model**, trained without explicit regularization.\n",
    "- An **optimized logistic regression model**, selected via cross-validation using **L2 regularization** and **C = 4.64**.\n",
    "\n",
    "The comparison is performed across several dimensions: classification metrics, ROC curves, model coefficients, predicted probability distributions, and individual error analysis.\n",
    "\n",
    "---\n",
    "\n",
    "### Overall Performance on Test Set\n",
    "\n",
    "| Model                         | Recall | F1-score | AUC   |\n",
    "|------------------------------|--------|----------|-------|\n",
    "| Simple LogReg                | 0.692  | 0.750    | 0.783 |\n",
    "| Optimized LogReg (L2, C=4.64)| 0.692  | 0.750    | 0.790 |\n",
    "\n",
    "- Both models achieve **identical recall and F1-score**.\n",
    "- The **optimized model** achieves a **slightly better AUC** (+0.007), indicating a marginal improvement in discriminative capacity.\n",
    "\n",
    "---\n",
    "\n",
    "### ROC Curve Comparison\n",
    "\n",
    "- The ROC curves are **almost superimposed**, confirming similar discriminative performance.\n",
    "- The optimized model achieves a **slightly higher AUC** (0.790 vs. 0.783), but the gain remains modest.\n",
    "\n",
    "---\n",
    "\n",
    "### Coefficient Comparison\n",
    "\n",
    "- The **L2-regularized model** produces **dense coefficients** (no exact zeros), but with slightly more constrained magnitudes.\n",
    "- Notable changes:\n",
    "  - Features like `Insulin_log` and `HOMA_log` are **slightly downweighted**.\n",
    "  - `Glucose` and `BMI` remain major contributors in both models.\n",
    "- This confirms that **L2 regularization stabilizes weights** without enforcing sparsity.\n",
    "\n",
    "---\n",
    "\n",
    "### Predicted Probabilities\n",
    "\n",
    "- Both models produce **comparable probability distributions** for the positive class.\n",
    "- The optimized model yields **more confident predictions** (closer to 0 or 1), suggesting **enhanced separation** and **greater decision certainty**.\n",
    "\n",
    "---\n",
    "\n",
    "### Error Analysis\n",
    "\n",
    "We examined the predictions for cases **misclassified by at least one model**:\n",
    "\n",
    "- Most predictions match across models.\n",
    "- A few **borderline examples** are classified differently, possibly reflecting subtle shifts in the **decision boundary** induced by regularization.\n",
    "\n",
    "---\n",
    "\n",
    "### Final Remarks\n",
    "\n",
    "| Model                   | Key Strength                         |\n",
    "|-------------------------|---------------------------------------|\n",
    "| Simple LogReg           | Simpler, marginally faster            |\n",
    "| Optimized LogReg (L2)   | More robust, better generalization    |\n",
    "\n",
    "- Both models are **viable** and offer **equivalent predictive performance** on this dataset.\n",
    "- The **L2-regularized model** is preferable when **stability**, **generalization**, or **coefficient shrinkage** are desired — even if no sparsity is enforced.\n"
   ]
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