Mathematics

Each lecture requires 2 hrs; 12 lectures + 4 labs = 36 hours (7 weeks: 19/10 - 4/12)

1. The multivariate Gaussian distribution: conditionals, marginals, and conjugate prior (and its problems)
2. Laplace method and Fisher matrix
3. Linear/ Gaussian models: probabilistic PCA and linear regression. Basis function regression.
4. Gaussian processes for regression and Bayesian Optimization.
5. Lab 1: linear regression and Gaussian Processes
6. Bayesian inference in non-conjugate models: Markov Chain Monte Carlo (MCMC), rejection and importance sampling, Metropolis-Hastings algorithm. Convergence diagnostics and rules of thumb.
7. Generalised linear models (GLMs) and inference; Gaussian processes for classification.
8. Lab 2: Bayesian GLMs.
9. Graphical models and hierarchical Bayesian models. Gibbs sampling.
10. Mixture models and topic models.
11. Variable augmentation: probit and logistic regression with auxiliary variables
12. Lab 3: Gibbs sampling for mixture models.
13. Variational inference: prelude, the EM algorithm
14. Mean-field variational inference
15. Variational inference for general models: black-box variational inference and variational autoencoders, Stein variational inference.
16. Lab 4: Variational mean field for mixture models.

Please, notice that this is a course belonging to Data Science Excellence Department programme. MAMA PhD students can plan 33% of their credits (i.e. 50 hrs) from this programme.