# Bayesian machine learning

**Lecturer:** Alexey Zaytsev (Visiting Assistant Research Fellow)

**Time:** 17:05 - 18:40 , Thu , 10/27/2022 - 1/12/2023

**Venue: **1110

**Online:** : 928 682 9093 PW: BIMSA

**Record:** Yes

**Level:** Graduate

**Language:** English

**Prerequisite**

Probability theory, Mathematical statistics, Machine learning

**Abstract**

Probabilistic approach in machine and deep learning leads to principled solutions. It provides explainable decisions and new ways for improving of existing approaches. Bayesian machine learning consists of probabilistic approaches that rely on Bayes formula. It can help in numerous applications and has beautiful mathematical concepts behind. In this course, I will describe the foundations of Bayesian machine learning and how it works as a part of deep learning framework.

**Reference**

The topic of the course is on the edge of the current advances in the field. We would provide a list of articles and books for each particular lecture. Good starting points are:

1. C. Bishop “Pattern Recognition and Machine learning”, 2006. Blocks 1 and 2.

2. C. Rasmussen “Gaussian processes for Machine learning”, 2005. Block 3

Tools: Notebook with access to colab.google.com

**Syllabus**

Block 1: Basics of Bayesian approach

Lecture 1. Reminder of mathematical statistics. Maximum likelihood approach. Bayesian linear regression

Lecture 2. Exponential family of distributions. Conjugate priors.

Lecture 3. Bayesian logistic regression. Laplace approximation.

Lecture 4. Bernstein-von-Mises theorem. Non-informative and reference priors.

Block 2: Approximate inference

Lecture 5. Variational inference. ELBO lower bound.

Lecture 6. Normalizing flows. Expectation propagation.

Lecture 7. Sampling problem statement. Importance sampling

Lecture 8. Monte-Carlo sampling. MCMC. Metropolis–Hastings algorithm. Hamiltonian Monte-Carlo.

Block 3: Gaussian process models

Lecture 9. Gaussian process regression. Exact inference scheme. Connection to RKHS space

Lecture 10. Approximate Generalized Gaussian process models. Heteroscedasticity modeling. Efficient Gaussian process regression. Fourier features. Nystrom approximation.

Lecture 11. Risk estimation for Gaussian process regression. Parametric and non-parametric approaches.

Block 4: Bayesian neural networks

Lecture 12. Neural networks basics. Bayesian dropout.

Lecture 13. Uncertainty estimation in machine learning: Bayesian and non-Bayesian methods

Lecture 14. Loss surfaces for deep neural networks.

Block 5: Point processes

Lecture 15. Basics: Poisson processes, non-homogenous Poisson process. Maximum likelihood estimation

Lecture 16. Hawkes process. Deep Hawkes processes based on RNNs and Transformers.

**Lecturer Intro**

Alexey has deep expertise in machine learning and processing of sequential data. He publishes at top venues, including KDD, ACM Multimedia and AISTATS. Industrial applications of his results are now in service at companies Airbus, Porsche and Saudi Aramco among others.

**Lecturer Email:** __A.Zaytsev@skoltech.ru__

**TA:** Dr. Miao He, __paris.muse7@gmail.com__