A rigorous 9-module deep dive into the internal mathematics and algorithmic mechanics of supervised learning: from OLS linear/polynomial regression and logistic log-loss to CART trees, Random Forests, Gradient Boosting (XGBoost/LightGBM/CatBoost), SVM duality, KNN geometry, Naive Bayes probability, and Multi-Layer Perceptron backpropagation.
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Ordinary Least Squares matrix derivation, gradient descent vs normal equation, Gauss-Markov theorem, and polynomial basis expansion.
Sigmoid activation mechanics, log-odds logit link function, Maximum Likelihood via Binary Cross-Entropy, and multiclass Softmax.
Recursive binary partitioning, Gini impurity vs Shannon entropy, Cost-Complexity Pruning (ccp_alpha), and tree variance properties.
Bootstrap aggregation math, feature subsampling variance reduction, Out-of-Bag (OOB) error estimation, and MDI vs permutation importance.
Gradient descent in functional space, pseudo-residuals, learning rate shrinkage, and architectural comparisons of XGBoost/LightGBM/CatBoost.
Geometric margin maximization, KKT conditions, primal-to-dual Lagrangian derivation, slack variables, and Mercer's kernel condition.
Minkowski distance metrics, curse of dimensionality mathematical proof, decision boundaries, and spatial indexing with KD-Trees.
Bayes' theorem derivation, conditional independence assumptions, Laplace smoothing, and Gaussian vs Multinomial vs Bernoulli models.
Forward tensor algebra, non-linear activations, multivariate matrix calculus backpropagation derivation, and He weight initialization.