Probability theory: sample spaces, sigma algebras, probability functions
The three axioms of probability
NO proofs involving set theory
Definition of conditional probability
Marginalization, Law of Total Probability
Product rule, chain rule
Independence and conditional independence of events
Random variables
Independence and conditional independence of random variables
Bayes rule
Basic discrete distributions: bernoulli, binomial, categorical, multinomial
Parametric distribution; parameters of distributions
Expected value of a random variable
Querying joint distributions
Efficiency of storage in joint distributions as tables
Rationale for directed grpahical models
Directed graphical models as joint distributions
Visual language of directed graphical models
Reading independence and conditional independence in a directed graphical model
Reading influence / information flow in a directed graphical model
VERY IMPORTANT: Answering questions on directed graphical models: joint queries, marginal queries, conditional queries
Efficiency of answering conditional queries
Text classification
Other kinds of classification problems
“Bag-of-words” assumption
VERY IMPORTANT: Naive Bayes as a directed graphical model, classifying with Naive Bayes, shortcomings of Naive Bayes models
Various event models for Naive Bayes: multivariate bernoulli, multivariate categorical, multinomial (especially multivariate categorical)
Class-conditional language models as classifiers
Evaluating classifiers
Maximum likelihood estimation for the categorical distribution
NO Lagrange Multipliers
The purpose and shapes and parametrization of the Beta distribution
The purpose and shapes and parametrization of the Dirichlet distribution
NO analytical forms of the Beta and Dirichlet distribution
Beta-Binomial conjugacy
Dirichlet-Multinomial conjugacy
NO Completing the integral
Point estimates to summarize the posterior distribution
Maximum a Posteriori (MAP) parameter estimation for the categorical distribution
Relationship between MAP estimation and add-one smoothing
Reading generative stories from a directed graphical model
Plate notation
High-level steps of the Expectation Maximization algorithm