The EM Algorithm - ML over Mixture of Distributions: mixture of binomial distributions, derivation of EM for general data, the EM rule for i.i.d. data, the coins example, mixture of normal distributions, the "bag of words" application.

Support Vector Machines and Kernel Functions: 2-class classification, separating hyperplane with maximal margin, derivation of SVM, SVM with Kernels, primer on constrained optimization.

Spectral Analysis I: PCA, LDA, CCA. Principle Component Analysis (PCA), multi-class
learning using Linear Discriminant Analysis (LDA) and Canonical Correlation Analysis (CCA).

The Formal (PAC) Learning Model: The formal learning model, the "rectangle learning problem", Learnability of Finite Concept Classes (realizable and unrealizable cases).

VC Dimension: definition and examples of VC-dimension, VC-dim and PAC learning, growth function Sauer's lemma.

Generalization theorems: A Polynomial Bound on the Sample Size m for PAC Learning, the double-sampling theorem.