Section 3: Advanced Topics for ML
Overview
Focus on probability and statistics concepts that appear frequently in modern machine learning theory and practice: exponential families, information theory, and concentration inequalities.
Topics Covered
Chapter 1: Exponential Families
- Exponential family canonical form
- Natural parameters and sufficient statistics
- Conjugate priors for exponential families
- Connection to generalized linear models (GLMs)
Chapter 2: Information Theory
- Entropy and cross-entropy
- KL divergence and its properties
- Mutual information
- Connections to ML loss functions (cross-entropy loss, ELBO)
Chapter 3: Limit Theorems and Concentration
- Law of large numbers (weak and strong)
- Central limit theorem
- Markov, Chebyshev, Hoeffding, and Chernoff inequalities
- Connection to PAC learning bounds
Learning Objectives
- Write common distributions in exponential family form
- Compute entropy, cross-entropy, and KL divergence
- Apply concentration inequalities to bound probabilities
- Connect limit theorems and concentration to ML generalization