Graphical Models

This course provides a comprehensive introduction to graphical models as a framework for representing, analysing, and learning complex dependency structures in multivariate data. Graphical models combine probability theory, statistics, and graph theory to provide interpretable representations of relationships among variables and to facilitate statistical inference in high-dimensional systems. Students are introduced to the principles of conditional independence and the graphical representations that encode these relationships. Both undirected and directed graphical models are studied, together with their associated Markov properties and factorization rules.

A substantial part of the course focuses on statistical modelling and network inference. Students learn graphical log-linear models for categorical data, Gaussian graphical models for continuous data, and modern approaches for high-dimensional network estimation such as graphical lasso, penalized likelihood methods, Bayesian structural learning, and cross-validation-based model selection. The course also covers copula graphical models and methods for handling mixed and non-Gaussian data.

The course further explores directed graphical models and causal graphical models, providing students with tools to distinguish statistical association from causal relationships. Topics include structural causal models, interventions, adjustment strategies, confounding, causal effect estimation, and causal discovery from observational data. By the end of the course, students will be able to construct, estimate, interpret, and critically evaluate graphical models for complex data, and apply modern network and causal inference methods to challenging scientific and societal problems.

• Represent complex dependency structures using graphical models, including undirected graphs, directed acyclic graphs (DAGs), chain graphs, and causal graphical models.
• Interpret and derive conditional independence relationships using graph-theoretic concepts such as separation, d-separation, factorization, Markov properties, and moralization.
• Model multivariate categorical, continuous, and mixed data through graphical log-linear models, Gaussian graphical models, copula graphical models, and directed graphical models.
• Estimate graphical model parameters and network structures using maximum likelihood methods, penalized likelihood approaches, graphical lasso, Bayesian structural learning, and related computational techniques.
• Perform model selection and assess model adequacy through hypothesis testing, information criteria, cross-validation, goodness-of-fit diagnostics, and regularization methods.
• Analyze high-dimensional networks and complex systems arising in fields such as biology, genomics, finance, medicine, social sciences, and engineering.
• Reason about causal mechanisms using graphical representations, including interventions, causal effects, adjustment strategies, confounding, causal discovery, and structural causal models.
• Apply graphical modelling techniques to real-world data, critically evaluating modelling assumptions, uncertainty, and the strengths and limitations of network-based statistical inference.

• Quality education
• Industry, innovation and infrastructure

In presence

Lectures and tutorials

Midterm and Final exam