Instructors

Antonino Abbruzzo

Department of Economics, Business and Statistics, University of Palermo

Federico Castelletti

Department of Statistics, Università Cattolica del Sacro Cuore

Outline

This course aims at introducing probabilistic graphical models, which provide a unified framework for learning dependence relationships between random variables and making statistical inference under complex multivariate settings. Participants will learn the fundamentals of graphical models, including Bayesian Networks and Markov Random Fields, and explore applications in machine learning, data analysis, and decision-making.

Teaching Methodology:

• Theoretical notions and statistical methodologies will be introduced throughout the lectures
• Participants will engage in practical exercises using popular graphical modeling tools
• Real-world applications and case studies will be explored to connect theory with practice

Additional Resources:

Textbooks and Readings:

• Introduction to graphical modelling (Edwards, D.)
• Handbook of Graphical Models (Maathuis, M. et al.)

Software Textbooks:

• Graphical Models with R (Hojsgaard, S. et al.)
• Bayesian Networks: With examples in R (Scutari, M. and Denis, J.B.)
• BCDAG: An R package for Bayesian structure and Causal learning of Gaussian DAGs (Castelletti, F. and Mascaro, A.)

Prerequisites

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• Basic understanding of probability theory and familiarity with concepts in linear algebra.
• Consolidated knowledge of the R software is also required.

Data set

TBA.

Schedule

Module 1

Session 1: Introduction to Graphical Models (09:00 - 10:30)

• Overview of graphical models and their applications
• Conditional Independence, Markov Properties, Factorization

Session 2: Bayesian Networks for Discrete Random Variables (11:00 - 12:30)

• Definition and representation of Bayesian Networks
• Building and Using Bayesian Networks
• Structural Learning and Model Selection of Bayesian Networks

Session 3: Markov Random Fields (14:00 - 15:30)

• Definition and representation
• Log-linear graphical models
• Model Checking and Answering Queries

Session 4: Practical (16:00 - 17:30)

• Analysis of a Dataset

Module 2

Session 1: Gaussian Graphical Models (09:00 - 10:30)

• Multivariate Normal distribution: properties and conditional independencies
• Gaussian Undirected Graphs (UGs) and Directed Acyclic Graphs (DAGs)

Session 2: Frequentist Methods for Structure Learning (11:00 - 12:30)

• The Graphical lasso for UG model selection
• Greedy search and Hill Climbing algorithm for DAG model selection

Session 3: Bayesian Structure Learning (14:00 - 15:30)

• Priors for Bayesian graphical model comparison
• Markov Chain monte Carlo algorithms for Bayesian structure learning

Session 4: Practical (16:00 - 17:30)

• Real data analyses

Software Installation

We will give you access to training computers with all the necessary software installed. However, if you want to run the analysis on your own computer, you can follow these instructions.

• Download and install R: https://cloud.r-project.org/
  • (Windows users): Download and install RTools: https://cran.r-project.org/bin/windows/Rtools/
• Download and install RStudio: https://www.rstudio.com/products/rstudio/download/#download