{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "First I am loading the data. I have to import the required libraries.\n", "\n", "\n", "1. **`numpy`** – Numerical computing, array operations. \n", "2. **`pandas`** – Data manipulation, handling tables (DataFrames). \n", "3. **`statsmodels.api`** – Statistical modeling, hypothesis testing, logistic regression. \n", "4. **`matplotlib.pyplot`** – Basic plotting and visualization. \n", "5. **`seaborn`** – Advanced statistical data visualization. \n", "6. **`StandardScaler` (from `sklearn.preprocessing`)** – Feature scaling (standardization). \n", "7. **`VarianceThreshold` (from `sklearn.feature_selection`)** – Removes low-variance features. \n", "8. **`LogisticRegression` (from `sklearn.linear_model`)** – Implements logistic regression for classification. \n" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Index(['id', 'diagnosis', 'radius_mean', 'texture_mean', 'perimeter_mean',\n", " 'area_mean', 'smoothness_mean', 'compactness_mean', 'concavity_mean',\n", " 'concave points_mean', 'symmetry_mean', 'fractal_dimension_mean',\n", " 'radius_se', 'texture_se', 'perimeter_se', 'area_se', 'smoothness_se',\n", " 'compactness_se', 'concavity_se', 'concave points_se', 'symmetry_se',\n", " 'fractal_dimension_se', 'radius_worst', 'texture_worst',\n", " 'perimeter_worst', 'area_worst', 'smoothness_worst',\n", " 'compactness_worst', 'concavity_worst', 'concave points_worst',\n", " 'symmetry_worst', 'fractal_dimension_worst', 'area_mean_category',\n", " 'area_se_category', 'area_worst_category', 'compactness_mean_category',\n", " 'compactness_se_category', 'compactness_worst_category',\n", " 'concave points_mean_category', 'concave points_se_category',\n", " 'concave points_worst_category', 'concavity_mean_category',\n", " 'concavity_se_category', 'concavity_worst_category',\n", " 'fractal_dimension_mean_category', 'fractal_dimension_se_category',\n", " 'fractal_dimension_worst_category', 'perimeter_mean_category',\n", " 'perimeter_se_category', 'perimeter_worst_category',\n", " 'radius_mean_category', 'radius_se_category', 'radius_worst_category',\n", " 'smoothness_mean_category', 'smoothness_se_category',\n", " 'smoothness_worst_category', 'symmetry_mean_category',\n", " 'symmetry_se_category', 'symmetry_worst_category',\n", " 'texture_mean_category', 'texture_se_category',\n", " 'texture_worst_category'],\n", " dtype='object')\n" ] }, { "data": { "image/png": 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", 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Matplotlib inlie\n", "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "\n", "#Model Imports\n", "from sklearn.linear_model import LinearRegression\n", "from sklearn.linear_model import LogisticRegression\n", "\n", "\n", "\n", "#Metric Imports\n", "from sklearn import metrics\n", "\n", "# Load Breast Cancer dataset\n", "\n", "df = pd.read_csv(r\"C:\\Users\\zahra\\Downloads\\breast-cancer-categorized.csv\")\n", "df.head()\n", "\n", "print(df.columns)\n", "\n", "# Scatter plot with correct labels\n", "plt.scatter(df['concavity_worst'], df['diagnosis'])\n", "plt.ylabel(\"Malignant (1) or Benign (0)\", fontsize=12)\n", "plt.xlabel(\"Concavity_Worst\", fontsize=12)\n", "plt.show()\n", "\n", "df['diagnosis'] = df['diagnosis'].map({'M': 1, 'B': 0})\n", "\n", "x=df['concavity_worst'].values.reshape(-1,1)\n", "y=df['diagnosis']\n", "\n", "lr=LinearRegression()\n", "lr.fit(x,y)\n", "predictions=lr.predict(x)\n", "plt.scatter(df['concavity_worst'], df['diagnosis'])\n", "plt.plot(df['concavity_worst'], predictions, color='red')\n", "\n", "plt.ylabel(\"Malignant (1) or Benign (0)\", fontsize=12)\n", "plt.xlabel(\"Concavity_Worst\", fontsize=12)\n", "plt.show()\n", "\n", "def sigmoid(x):\n", " a=[]\n", " for item in x:\n", " a.append(1/(1+np.exp(-item)))\n", " return a\n", "x=np.arange(-10.,10.,0.2)\n", "sig=sigmoid(x)\n", "plt.plot(x,sig)\n", "\n", "\n", "\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "WARNING (pytensor.configdefaults): g++ not available, if using conda: `conda install gxx`\n", "WARNING (pytensor.configdefaults): g++ not detected! PyTensor will be unable to compile C-implementations and will default to Python. Performance may be severely degraded. To remove this warning, set PyTensor flags cxx to an empty string.\n" ] }, { "data": { "image/png": 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", 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       "
\n" ], "text/plain": [ "\n" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 1625 seconds.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "Bayesian Parameter Estimates (95% HDI):\n", " mean sd hdi_2.5% hdi_97.5% mcse_mean mcse_sd ess_bulk \\\n", "intercept -0.650 0.124 -0.893 -0.415 0.002 0.002 3954.0 \n", "slope 2.442 0.200 2.062 2.845 0.004 0.003 3244.0 \n", "\n", " ess_tail r_hat \n", "intercept 2691.0 1.0 \n", "slope 2678.0 1.0 \n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "import pymc as pm\n", "from sklearn.linear_model import LogisticRegression\n", "\n", "# Load Breast Cancer dataset\n", "df = pd.read_csv(r\"C:\\Users\\zahra\\Downloads\\breast-cancer-categorized.csv\")\n", "\n", "# Encode diagnosis\n", "df['diagnosis'] = df['diagnosis'].map({'M': 1, 'B': 0})\n", "\n", "# Prepare data\n", "x = df['concavity_worst'].values.reshape(-1, 1)\n", "y = df['diagnosis'].values\n", "\n", "# Train logistic regression model\n", "logreg = LogisticRegression(C=1000)\n", "logreg.fit(x, y)\n", "\n", "# Predict probabilities\n", "probabilities = logreg.predict_proba(x)[:, 1]\n", "\n", "# Create DataFrame for plotting\n", "example_df = pd.DataFrame({\n", " 'concavity_worst': df['concavity_worst'],\n", " 'diagnosis': y,\n", " 'logistic_preds': probabilities\n", "})\n", "\n", "# Sort by concavity_worst for smooth plotting\n", "example_df = example_df.sort_values('concavity_worst')\n", "\n", "# Plot\n", "plt.figure(figsize=(8, 5))\n", "plt.scatter(example_df['concavity_worst'], example_df['diagnosis'], label='Actual Diagnosis', alpha=0.5)\n", "plt.plot(example_df['concavity_worst'], example_df['logistic_preds'], color='red', label='Logistic Fit')\n", "plt.xlabel('Concavity Worst')\n", "plt.ylabel('Malignant (1) / Benign (0)')\n", "plt.title('Logistic Regression on Breast Cancer Diagnosis')\n", "plt.legend()\n", "plt.grid(True)\n", "plt.show()\n", "\n", "Score=logreg.score(x,y)\n", "print(Score)\n", "\n", "# --- Bootstrap Confidence Interval Estimation ---\n", "\n", "from sklearn.utils import resample\n", "\n", "n_iterations = 1000\n", "coefs = []\n", "\n", "for i in range(n_iterations):\n", " # Resample data with replacement\n", " x_resampled, y_resampled = resample(x, y)\n", "\n", " # Fit logistic regression on resampled data\n", " model = LogisticRegression(C=1000)\n", " model.fit(x_resampled, y_resampled)\n", "\n", " # Save the coefficient (model.coef_ is 2D array)\n", " coefs.append(model.coef_[0][0])\n", "\n", "# Calculate 2.5 and 97.5 percentiles for 95% CI\n", "lower_bound = np.percentile(coefs, 2.5)\n", "upper_bound = np.percentile(coefs, 97.5)\n", "\n", "print(\"\\n95% Confidence Interval for coefficient (bootstrapped):\")\n", "print(f\"[{lower_bound:.4f}, {upper_bound:.4f}]\")\n", "\n", "\n", "import statsmodels.api as sm\n", "\n", "# Add intercept (statsmodels doesn't add it by default)\n", "x_with_const = sm.add_constant(x)\n", "\n", "# Fit logistic regression model using statsmodels\n", "logit_model = sm.Logit(y, x_with_const)\n", "result = logit_model.fit(disp=False)\n", "\n", "# Get parameters and 95% CI (Wald method)\n", "params = result.params\n", "conf = result.conf_int()\n", "\n", "print(\"\\nWald Method:\")\n", "print(\"Coefficient:\", params[1])\n", "lower_ci, upper_ci = conf[1]\n", "print(\"95% CI:\", [lower_ci, upper_ci])\n", "\n", "\n", "from scipy.stats import chi2\n", "\n", "# Function to compute log-likelihood with fixed slope\n", "def log_likelihood_fixed_coef(beta1_fixed, x, y):\n", " x_with_const = sm.add_constant(x)\n", " # Replace the slope with fixed value, keep intercept as free param\n", " def llfun(beta0): # only optimize intercept\n", " linear_pred = beta0 + beta1_fixed * x.flatten()\n", " prob = 1 / (1 + np.exp(-linear_pred))\n", " return np.sum(y * np.log(prob + 1e-10) + (1 - y) * np.log(1 - prob + 1e-10))\n", "\n", " from scipy.optimize import minimize_scalar\n", " res = minimize_scalar(lambda b0: -llfun(b0)) # maximize log-likelihood\n", " return -res.fun # return maximum log-likelihood\n", "\n", "# Full model log-likelihood\n", "full_model_ll = result.llf\n", "\n", "# Test values around the estimated coefficient\n", "beta1_hat = result.params[1]\n", "beta1_vals = np.linspace(beta1_hat - 1, beta1_hat + 1, 100)\n", "\n", "# Likelihood ratio values\n", "lr_stats = []\n", "\n", "for b1 in beta1_vals:\n", " ll_fixed = log_likelihood_fixed_coef(b1, x, y)\n", " lr = 2 * (full_model_ll - ll_fixed)\n", " lr_stats.append(lr)\n", "\n", "# 95% threshold from chi-square distribution with 1 df\n", "threshold = chi2.ppf(0.95, df=1)\n", "\n", "# Find values where likelihood ratio is below threshold\n", "ci_vals = [b for b, lr in zip(beta1_vals, lr_stats) if lr < threshold]\n", "\n", "if ci_vals:\n", " lower_lr, upper_lr = min(ci_vals), max(ci_vals)\n", " print(\"\\nLikelihood Ratio CI for coefficient:\")\n", " print(f\"95% CI: [{lower_lr:.4f}, {upper_lr:.4f}]\")\n", "else:\n", " print(\"Could not determine CI from likelihood ratio.\")\n", "\n", "\n", " #Bayesian Estimator\n", "\n", "import pymc as pm\n", "import arviz as az\n", "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "from sklearn.linear_model import LogisticRegression\n", "\n", "# Load Breast Cancer dataset\n", "df = pd.read_csv(r\"C:\\Users\\zahra\\Downloads\\breast-cancer-categorized.csv\")\n", "\n", "# Encode diagnosis\n", "df['diagnosis'] = df['diagnosis'].map({'M': 1, 'B': 0})\n", "\n", "# Prepare data\n", "x = df['concavity_worst'].values.reshape(-1, 1)\n", "y = df['diagnosis'].values\n", "\n", "# Train logistic regression model\n", "logreg = LogisticRegression(C=1000)\n", "logreg.fit(x, y)\n", "\n", "# Predict probabilities\n", "probabilities = logreg.predict_proba(x)[:, 1]\n", "\n", "# Create DataFrame for plotting\n", "example_df = pd.DataFrame({\n", " 'concavity_worst': df['concavity_worst'],\n", " 'diagnosis': y,\n", " 'logistic_preds': probabilities\n", "})\n", "\n", "# Standardize x for better numerical stability\n", "x_std = (x - x.mean()) / x.std()\n", "\n", "# Bayesian Estimator with PyMC\n", "with pm.Model() as logistic_model:\n", " # Priors for intercept and slope\n", " intercept = pm.Normal(\"intercept\", mu=0, sigma=5)\n", " slope = pm.Normal(\"slope\", mu=0, sigma=5)\n", "\n", " # Logistic model\n", " logits = intercept + slope * x_std.flatten()\n", " theta = pm.Deterministic(\"theta\", pm.math.sigmoid(logits))\n", "\n", " # Likelihood\n", " y_obs = pm.Bernoulli(\"y_obs\", p=theta, observed=y)\n", "\n", " # Sampling\n", " trace = pm.sample(1000, tune=1000, target_accept=0.9, progressbar=True)\n", "\n", "# Summarize the posterior distributions\n", "summary = az.summary(trace, var_names=[\"intercept\", \"slope\"], hdi_prob=0.95)\n", "print(\"\\nBayesian Parameter Estimates (95% HDI):\")\n", "print(summary)\n", "\n", "# Optional: Plot the posterior distributions\n", "az.plot_posterior(trace, var_names=[\"intercept\", \"slope\"])\n", "plt.show()\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ] } ], "metadata": { "kernelspec": { "display_name": "base", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.7" } }, "nbformat": 4, "nbformat_minor": 2 }