Probabilistic Machine Learning and Pattern Recognition

Recommended Prerequisites

Linear Algebra,  Probabilities and Statistics, Programming (e.g. Python, R, Matlab, C++, Java, Julia)

Teaching Methods

This UC will have lectures with slides and with laboratory work using interactive tools (e.g. Jupyter notebook). Students will always work manually each module, during and after the theoretical class, to assimilate new concepts. It is designed to be incremental, and strongly supported with practice.

Learning Outcomes

A student who has met the objectives of the UC will be able to:
- Explain central concepts such as Probabilistic Graphical Modeling (PGM), prior, posterior, likelihood, Bayesian inference and belief propagation
- Understand and be able to manipulate the different blocks of a probabilistic program
- Recognise usages for the different probabilistic graphical models presented in the course and explain their underlying assumptions
- Formulate a new model, given a problem specification and its data
- Apply the different inference methods available in the studied tools
- Explain practical data modeling aspects, like overfitting, system (e.g. spatial-temporal) dynamics, conditional independence, imputation, conjugate prior
- Evaluate the quality of different models for a given problem and data
- Present, and be able to argue for, a project based on PGM
- Relate existing problems and data (e.g. from specific domains) with modelling approaches to tackle them

Work Placement(s)

No

Syllabus

1- Review of basics – random variable, probability distributions, Bayes Theorem
2- Probabilistic Graphical Models foundations – Bayesian networks, factorization,
conditional independence
3- Probabilistic Graphical Models – Generative models, Representing your own problem 
- Different models – Regression, Classification, Temporal models, Topic Models
4- Inference – Exact Inference
5- Inference – Markov Chain Monte Carlo
6- Inference – Variational Inference
7- Advanced Topics

Head Lecturer(s)

Joel Perdiz Arrais

Assessment Methods

Assessment
Exam: 50.0%
Project: 50.0%

Bibliography

"Model Based Machine Learning", John Winn, Christopher Bishop, Thomas Diethe, http://www.mbmlbook.com
"Probabilistic Graphical Models", Daphne Koller and Nir Friedman
"Pattern Recognition and Machine Learning", Christopher Bishop
"Bayesian Reasoning and Machine Learning2, David Barber, 2015