While selected material from the resources below may form part of the compulsory reading, the material is generally **not** required reading. In particular, you will not need to procure any books for the course.

### Additional support for the lectures

This is a collection of additional material that may help you to better understand the lectures. Advanced material, sometimes going well beyond the scope of PMR, is marked with a ⚠.

#### Background

- MLPR math background
- MLPR background on expectation/average
- Koller's video on probability distributions
- Koller's video on statistical independence
- Koller's overview on probabilistic graphical models
- Barber: Chapter 1

#### Directed graphical models

- Koller's introduction to directed graphical models (Bayesian networks)
- Koller's video on reasoning patterns
- Koller's video on flow of probabilistic influence/introduction to d-separation
- Koller's video on independencies in directed graphical models
- Koller's video on Naive Bayes
- Koller's video on application to medical diagnosis
- Bishop Sections 8.1 and 8.2
- Barber: Chapter 2, Sections 3.1 and 3.3 (without 3.3.6)
- Section 2.1 in Michael Jordan's "An Introduction to Probabilistic Graphical Models"

#### Undirected graphical models

- Koller's video on factors
- Koller's video on Gibbs distributions
- Koller's video on pairwise Markov networks
- Koller's video on independencies in Markov networks
- Bishop: Section 8.3
- Barber: Section 4.1, 4.2
- Section 2.2 in Michael Jordan's "An Introduction to Probabilistic Graphical Models"

#### Causality and Graphical Models

#### Expressive power and comparison between directed and undirected graphical models

- Koller's video on I-maps and perfect maps
- Barber: Section 4.5
- Chapter 4 of Michael Jordan's "An Introduction to Probabilistic Graphical Models" (file is provided as chapter16.ps) ⚠

#### Factor graphs

- Bishop: Section 8.4.3
- Barber: Section 4.4
- Research paper "Extending Factor Graphs so as to Unify Directed and Undirected Graphical Models", UAI 2003, by B. Frey ⚠

#### Exact inference

- MLPR notes on multivariate Gaussians
- Koller's video on (conditional) probability queries
- Koller's video on variable elimination
- Koller's video on the complexity of variable elimination
- Koller's video on graph-based perspective of variable elimination
- Koller's video on finding elimination orderings
- Koller's video on MAP inference
- Bishop: Section 8.4 till 8.4.6 on inference in graphical models
- Barber: Sections 5.1 to 5.4 on variable elimination, sum-product algorithm, etc; Section 23.1 on Markov chains, Section 23.2 on HMM inference
- Research paper "Factor Graphs and the Sum-Product Algorithm", 2001, by F. Kschischang et al. ⚠

#### Learning, factor analysis, and ICA

- Murphy's notes on conjugate Bayesian analysis of the Gaussian distribution
- Barber: Sections 9.1 to 9.4 on learning; Chapter 21 on factor and independent component analysis
- More details on PCA (Chapter 2) and background on linear algebra (Appendix A)
- ICA demo
- Advanced review on ICA by A. Hyvarinen ⚠

#### Score matching and other methods to estimate unnormalised models

- Review paper on further estimation methods for unnormalised models by M. Gutmann and A. Hyvarinen
- Original paper on score matching by A. Hyvarinen
- A general framework to estimate unnormalised models by M. Gutmann and J. Hirayama ⚠
- Noise-contrastive estimation to estimate unnormalised models by M. Gutmann and A. Hyvarinen ⚠
- Score matching for generative modelling by Y. Song and S. Ermon ⚠

#### Sampling and Monte Carlo

- Barber: Chapter 27
- Iain Murray's tutorial on Monte Carlo methods ⚠
- An Introduction to MCMC for Machine Learning by Andrieu et al ⚠
*Introducing Monte Carlo Methods with R*by Robert and Casella ⚠- Pareto Smoothed Importance Sampling by Vehtari et al ⚠ ⚠
- Art Owen's book
*Monte Carlo theory, methods and examples*⚠ ⚠ - Chopin and Papaspiliopoulos' book
*An Introduction to Sequential Monte Carlo*⚠ ⚠

#### Variational inference and EM algorithm

- Barber: Chapter 11
- Shakir Mohamed's tutorial on variational inference
- An Introduction to Variational Autoencoders by Kingma and Welling
- Variational Inference: A Review for Statisticians by Blei et al ⚠
- Advances in Variational Inference by Zhang et al ⚠

### Books

This is a list with general and specialised machine learning books. As indicated below, some of the books are available at the Library.

- Pattern Recognition and Machine Learning

Christopher Bishop

Springer 2006

(available online) - Probabilistic Graphical Models : Principles and Techniques

Daphne Koller and Nir Friedman

MIT Press 2009

(available at the University library) - Bayesian Reasoning and Machine Learning

David Barber

Cambridge University Press 2012

(available online) - Bayesian networks : an introduction

Timo Koski and John Noble

John Wiley 2009

(available at the University library) - Graphical models

Steffen L. Lauritzen

Oxford University Press 1996

(available at the University library) - Causal Inference in Statistics: A Primer. Judea Pearl, Madelyn Glymour, Nicholas P. Jewell, Wiley, 2016 (available via the University library)
- Probability and Statistics

Morris DeGroot and Mark Schervish

Pearson, 4th Edition

(available at the University library) - Information Theory, Inference, and Learning Algorithms

David J.C. MacKay

Cambridge University Press 2003

(available online) - The Matrix Cookbook

Petersen and Pedersen

(available online) - Graphical models and message-passing algorithms: Some introductory lectures

Martin J. Wainwright

(available online) - An Introduction to Probabilistic Graphical Models (incomplete draft)

Michael Jordan

(parts available online here and here) - Independent Component Analysis

Aapo Hyvarinen, Juha Karhunen, and Erkki Oja

(electronic copy available at the University library) - Monte Carlo Statistical Methods

Christian Robert and George Casella

Springer 2004 - Introducing Monte Carlo Methods with R

Christian Robert and George Casella

Springer 2010

(available at the University library) - Bayesian data analysis

Andrew Gelman, John B. Carlin, Hal S. Stern, David B. Dunson, Aki Vehtari, and Donald B. Rubin

CRC Press 2013

(available at the University library) - Mathematics for Machine Learning

Marc Peter Deisenroth, A. Aldo Faisal, Cheng Soon Ong

Cambridge University Press 2020

(available online) - An Introduction to Sequential Monte Carlo

Nicolas Chopin and Omiros Papaspiliopoulos

Springer 2020

(available at the University library) - Art Owen

Monte Carlo theory, methods and examples

(available online) - Probabilistic machine learning book series by Kevin Murphy

(available online)