This course teaches probabilistic graphical models and their inference algorithms.

Contents

1. Introduction
   1. Conjugate priors
   2. Linear Gaussian system
   3. The exponential family distribution
2. Bayesian statistics
   1. Bayesian statistics vs. frequentist statistics
   2. Bayesian model selection (BIC)
   3. Hierarchical Bayesian (Empirical Bayes)
3. Generalized linear models
   1. Bayesian linear regression
   2. Bayesian logistic regression
4. Directed graphical models
   1. d-separation
   2. Markov blanket
5. Mixture models and the EM algorithm
6. Gaussian process
   1. Kernels
   2. GP for regression
7. Markov and hidden Markov models
   1. Markov models
   2. Hidden Markov model
8. State space model
   1. Linear dynamical system
   2. Kalman filtering and smoothing
9. Markov random fields
   1. The Hammersley-Clifford theorem
   2. Ising model etc.
10. Variational Inference
    1. The mean field method
    2. Expectation propagation
11. Monte Carlo inference
    1. Sampling from standard distributions
    2. Rejection sampling (Adaptive rejection sampling)
    3. Importance sampling
12. MCMC
    1. Gibbs sampling
    2. Metropolis Hastings algorithm
    3. MCMC using Hamiltonian Dynamics
13. Clustering
    1. Dirichlet process mixture model
14. Structured data
    1. Restricted Boltzmann machines (contrastive divergence)
15. Online learning
    1. Multi-armed bandit
    2. Thompson sampling
    3. Bayesian optimization (expected improvement, entropy search)

References

1. Kevin Murphy, “Machine Learning: A probabilistic perspective”, 2012, MIT press