Why cross-entropy is the loss for probabilistic classifiers: the additive identity H(P,Q)=H(P)+KL(P||Q), the coin-flip derivation, the bridge to negative log-likelihood and maximum likelihood, binary/multiclass/soft-label forms, and stable logit-based implementation.

KL and Jensen-Shannon divergence for drift monitoring: what they measure, why direction and support matter, the divergence-vs-distance and log-base gotchas, and how to turn a drift score into a decision (not an automatic retrain).

Most models learn what normal looks like and then measure how far a point sits from it: a distance, a density, a reconstruction error. Isolation Forest takes the opposite route. It never models nor...

What ROC-AUC and PR-AUC (average precision) actually measure, why they diverge under class imbalance, how prevalence moves PR but not ROC, and how to pick a metric from the decision you need to make.

One-Class SVM for novelty detection: the separating-from-the-origin objective, what the RBF unit-sphere property does and does not prove, and the roles of nu and gamma.

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.