14-part comprehensive curriculum: statistical foundations, data preprocessing, regression, classification, ensembles, SVM, clustering, dimensionality reduction, evaluation metrics, and end-to-end scikit-learn workflows.
Formal definition of machine learning, mathematical formulation (hypothesis space, loss function, empirical risk), learning paradigms, hands-on first models, and end-to-end production workflow.
Core statistical learning principles: generalization vs training performance, empirical risk minimization, underfitting, overfitting, the bias-variance tradeoff decomposition, and learning curves.
Leak-proof data preparation: fit-on-train transform-everywhere golden rule, missing value imputation, robust feature scaling, categorical encoding, feature engineering, and automated ColumnTransformer.
Simple and multiple linear regression, Ordinary Least Squares (OLS) closed-form matrix derivation, gradient descent optimization, classical assumptions, residual diagnostics, and polynomial regression.
Binary and multiclass logistic regression, log-odds and logit functions, sigmoid activations, maximum likelihood estimation with binary cross-entropy, decision boundaries, and threshold tuning.
Controlling model complexity and multicollinearity: L2 Ridge regularization, L1 Lasso sparsity and feature selection, Elastic Net convex combinations, and regularization path visualizations.
Intuitive non-linear modeling and ensembles: splitting criteria (Gini impurity, Entropy), tree pruning, Bagging with Random Forests, AdaBoost, and Gradient Boosted Decision Trees (GBDT/XGBoost).
Geometric classification with maximum margin hyperplanes, soft margin optimization with slack variables, the dual Lagrangian formulation, and non-linear kernel tricks (RBF, Polynomial).
Instance-based learning and probabilistic models: k-Nearest Neighbors distance metrics, curse of dimensionality, Bayes Theorem, conditional independence assumptions, and Gaussian/Multinomial Naive Bayes.
Unsupervised pattern discovery: K-Means optimization and initialization heuristics (K-Means++), Hierarchical Agglomerative clustering, density-based DBSCAN, and Silhouette/Davies-Bouldin cluster validation.
High-dimensional feature space compression: Principal Component Analysis (PCA) via covariance eigendecomposition and SVD, explained variance ratio, and non-linear manifold projection with t-SNE.
Comprehensive performance measurement: Confusion matrices, Precision-Recall curves, ROC-AUC, F1-Score (micro/macro/weighted), and regression metrics (MAE, MSE, RMSE, R², Adjusted R²).
Systematic model optimization and validation: K-Fold cross-validation, Stratified K-Fold, exhaustive GridSearchCV, RandomizedSearchCV, Bayesian optimization, and leak-proof nested CV architectures.
Production-ready machine learning workflows: Scikit-learn BaseEstimator & TransformerMixin API, ColumnTransformer pipelines, feature unions, model persistence with Joblib, and deployment best practices.