Use the SVM dual's dependence on dot products to unlock non-linear boundaries: the kernel trick, the polynomial and RBF kernels, and practical tuning, multiclass, and regression.

Derive the SVM dual with Lagrange multipliers, see why the dual is often preferred over the primal, and read off the support vectors through the KKT conditions.

Build the linear SVM from hyperplane geometry: signed distance, the maximum-margin primal, why the boundaries are fixed at plus/minus one, and the soft-margin hinge-loss objective.

Derive Naive Bayes once, work a full numerical spam example in log space, tour the Bernoulli, Multinomial, Complement, Categorical, and Gaussian variants, and get the smoothing, MAP, and calibration story right.

Extend binary logistic regression to neural-network notation and multiclass softmax, then evaluate and train responsibly on imbalanced data.

Interpret logistic-regression coefficients and odds ratios, understand feature scaling and decision thresholds, and explore linear separability through XOR.

Derive binary logistic regression from log-odds and Bernoulli likelihood, then train it using cross-entropy and numerical optimization.

Evaluate linear regression with R-squared, handle outliers, interpret coefficients and feature importance, and extend the framework with GLMs.

Diagnose multicollinearity and understand how Ridge, Lasso, Elastic Net, and Bayesian priors stabilize or simplify linear regression.

Derive the normal equation and understand the statistical guarantees, assumptions, invariances, and singularity limits of ordinary least squares.