**Title:** Bayesian Machine Learning

**Lecturer:** Guido Sanguinetti, University of Edinburgh

**Place**: Computer Science Department, University of Pisa

**Period:**

- 23 February seminar room west 15 - 17;
- 24 /25 / 26 February seminar room west 9- 11;
- 27 February Laboratorio didattico Polo Fibonacci "I" 9 - 11;
- 2 March seminar room west 16 - 18;
- 3 / 4/ 5 March seminar room west 9- 11;
- 6 March Laboratorio didattico Polo Fibonacci "I" 9 - 11;

This is a rough summary for the Bayesian Machine Learning course. The main reference is D. Barber's book, Bayesian Reasoning and Machine Learning; the numbers in brackets refer to Barber's book unless explicitly stated otherwise. The book is available online from

http://web4.cs.ucl.ac.uk/staff/D.Barber/pmwiki/pmwiki.php?n=Brml.HomePage

**Lecture 1**: Statistical basics. Probability refresher, probability distributions, entropy and KL divergence (Ch 1, Ch 8.2, 8.3). Multivariate Gaussian (8.4). Estimators and maximum likelihood (8.6 and 8.7.3). Supervised and unsupervised learning (13.1)**Lecture 1****Lecture 2**: Linear models. Regression with additive noise and logistic regression (probabilistic perspective): maximum likelihood and least squares (18.1 and 17.4.1). Duality and kernels (17.3).**Lecture 2****Lecture 3**: Bayesian regression models and Gaussian Processes. Bayesian models and hyperparameters (18.1.1, 18.1.2). Gaussian Process regression (19.1-19.4, see also Rasmussen and Williams, Gaussian Processes for Machine Learning, MIT Press, 2007, Ch 2. Available for download at http://www.gaussianprocess.org/gpml/).**Lecture 3**- Lecture 4: Active learning and Bayesian optimisation. Active learning, basic concepts and types of active learning (B. Settles, Active learning literature survey, sections 2 and 3, available from http://burrsettles.com/pub/settles.activelearning.pdf.) Bayesian optimisation and the GP-UCB algorithm (Brochu et al, see http://arxiv.org/abs/1012.2599).
**Lecture 4** **Lab 1**: GP regression and Bayesian Optimisation.**Lecture 5**: Latent variables and mixture models. Latent variables and the EM algorithm (11.1 and 11.2.1). Gaussian mixture models and mixture of experts (20.3, 20.4).**Lecture 5****Lecture 6**: Graphical models. Belief networks and Markov networks (3.3 and 4.2). Factor graphs (4.4).**Lecture 6****Lecture 7**: Exact inference in trees. Message passing and belief propagation (5.1 and 28.7.1).**Lacture 7****Lecture 8**: Approximate inference in graphical models. Variational inference: Gaussian and mean field approximations (28.3, 28.4). Sampling methods and Gibbs sampling (27.4 and 27.3).**Lecture 8****Lab 2**: Bayesian Gaussian mixture models.