Professors: VICENÇ GÓMEZ

Description

Structured probabilistic models also known as probabilistic graphical models (PGMs) are powerful modeling tools for reasoning and decision making with uncertainty. PGMs have many application domains, including artificial vision, natural language processing, efficient coding, and computational biology. PGMs connect graph theory and probability theory and provide a flexible framework for modeling large collections of random variables with complex interactions.

This is an introductory course to PGMs focused on two main axes: (1) the role of PGMs as a unifying language in machine learning, which allows for a natural specification of many problematic domains with inherent uncertainty, and (2) the set of computational tools for probabilistic inference (such as making predictions to aid decision making) and learning (estimating the structure of the graph and its parameters from data).

At the end of the course, the student will be able to:

• Use probabilistic graphical models and statistical tools for modeling domain knowledge under uncertainty.
• Program basic algorithms for learning and inference in graphical models.
• Identify their role in real-world machine learning applications.
• Understand the difference between statistical and causal models.

Format

The course will combine seminar lectures with problem-solving sessions (both analytical and programming). The programming sessions will be in Matlab, following the BRML toolbox. The evaluation will be based on regular exercises and a final exam.

Contents

Block 1: Representation

• Directed graph models
• Undirected graph models
• Factor graph models

Block 2: Probabilistic Inference

• Exact inference: variable elimination
• Message passing algorithms. Belief Propagation
• The Junction tree algorithm
• Temporal models
• Approximate inference

Block 3: Learning

• Maximum likelihood and structural learning
• Introduction to causality

Teaching Methods

The course consists of ten sessions where the fundamental theoretical concepts and examples of problem solving are introduced and developed. Students should solve problems and implement some algorithms presented in the sessions. A small research project should be carried out to analyze a scientific article.

Associated skills

Basic skills

• Understand the knowledge that provides a basis or opportunity to be original in the development and / or application of ideas, often in a research context.
• That students know how to apply the knowledge acquired and their ability to solve problems in novel or poorly known environments within broader (or multidisciplinary) contexts related to their area of study.
• That students are able to integrate knowledge and face the complexity of making judgments based on information that, being incomplete or limited, includes reflections on social and ethical responsibilities linked to the application of their knowledge and judgments.
• That students have the learning skills that allow them to continue studying in a way that will need to be largely self-directed or autonomous.

Specific skills and learning outcomes

E1) Apply the models and algorithms of machine learning, autonomous systems, interaction in natural language, mobile robotics and / or web intelligence to a problem of well-identified interactive intelligent systems. Specifically, models and algorithms for inference and learning in structured graphical models.

• Solves problems related to interactive intelligent systems
• Identifies the appropriate models and algorithms to solve a specific problem in the field of interactive intelligent systems.
• Evaluates the result of applying a model or algorithm to a specific problem.
• Presents the result of the application of a model or algorithm to a specific problem according to scientific standards.

E3) Identify new uses of models and algorithms in the field of interactive intelligent systems. Specifically, uses for which structured graphical models are appropriate

• Recognizes the intentional domain of application of a model or algorithm in the field of interactive intelligent systems.
• Describes limitations of a given model or algorithm for a new problem.
• Identifies parallels in problems in the field of interactive intelligent systems.
• Transfers the solution of a specific problem in the field of interactive intelligent systems to a similar problem.

E6) Present the result of a research project in the field of interactive intelligent systems in a scientific forum and in
interaction with other researchers.

• Organizes and conducts an oral presentation of a research paper according to the rules of the discipline
• Carries out a scientific argument and convincingly defend scientific work in front of an expert and non-expert public.

Prerequisites

The course requires knowledge and skills in graph theory, probability and statistics, linear algebra and data manipulation.

Evaluation

The evaluation consist of an theory exam and homework exercises, including analytical problems and short programming tasks.

Final grade = 0.5 * Exam + 0.5 * Homework

The theory exam is an individual written exam that assesses the competencies developed throughout the course. There is a minimum grade (Exam > 4) to pass the course.

In case of failing the course, the student will have to attend a resit exam, but only if the homework is passed (Homework > 5). The final grade in this case is

Resit Grade = 0.5 * Resit Exam + 0.5 * Homework

Bibliography

[1] “Bayesian Reasoning and Machine Learning”, David Barber. Cambridge University Press. 2012.
[2] Probabilistic Graphical Models: Principles and Techniques. D. Koller & N. Friedman. MIT Press. 2009.
[3] “Bayesian networks and decision graphs”, Finn B. Jensen, Thomas Graven-Nielsen. Series: Information Science and Statistics. Springer. 2007.
[4] Pattern Recognition and Machine Learning (Chap. 8). C. Bishop. Springer. 2006.
[5] Information Theory, Inference, and Learning Algorithms. D. Mackay. Cambridge university press. 2003.

All the material will be available through the Aula Global