Syllabus

Day 1: Probability spaces

  1. Basic probability
  2. Multiple events, Bayes’ rule, independence
  3. Random variables, expectation and variance

Day 2: Discrete and continuous distributions: a variety of commonly-used distributions.

  1. Coin flips and the binomial distribution
  2. Multinomial
  3. Poisson and exponential
  4. The standard normal: “bell curve”
  5. Multivariate normal. Vector-valued observations, covariances.

Day 3: Basic statistical procedures

  1. Dimensionality reduction: principal component analysis and SVD
  2. Embedding: classic multidimensional scaling
  3. Regression: least-squares regression and ridge regression
  4. Classification: Fisher linear discriminant
  5. Conditional probability estimation: logistic regression

Day 4: Statistical testing

  1. Sampling and the central limit theorem
  2. Hypothesis testing: null hypothesis, p-values, A/B testing

Day 5: Probabilistic models

  1. Naive Bayes
  2. Mixtures of Gaussians
  3. Simple Bayesian nets
  4. Topic models