A graphical model is a statistical model that is represented by a graph. The factorization properties underlying graphical models facilitate tractable computation with multivariate distributions, making the models a valuable tool with a plethora of applications. Furthermore, directed graphical models allow intuitive causal interpretations and have become a cornerstone for causal inference.
While there exist a number of excellent books on graphical models, the field has grown so much that individual authors can hardly cover its entire scope. Moreover, the field is interdisciplinary by nature. Through chapters by leading researchers from different areas, this handbook provides a broad and accessible overview of the state of the art.
- Contributions by leading researchers from a range of disciplines
- Structured in five parts, covering foundations, computational aspects, statistical inference, causal inference, and applications
- Balanced coverage of concepts, theory, methods, examples, and applications
- Chapters can be read mostly independently, while cross-references highlight connections
The handbook is targeted at a wide audience, including graduate students, applied researchers, and experts in graphical models.
Part I: Conditional independencies and Markov properties.
1. Conditional Independence and Basic Markov Properties - Milan Studený
2. Markov Properties for Mixed Graphical Models - Robin Evans
3. Algebraic Aspects of Conditional Independence and Graphical Models - Thomas Kahle, Johannes Rauh, and Seth Sullivant
Part II: Computing with factorizing distributions
4. Algorithms and Data Structures for Exact Computation of Marginals - Jeffrey A. Bilmes
5. Approximate Methods for Calculating Marginals and Likelihoods - Nicholas Ruozzi
6. MAP Estimation: Linear Programming Relaxation and Message-Passing Algorithms - Ofer Meshi and Alexander G. Schwing
7. Sequential Monte Carlo Methods - Arnaud Doucet and Anthony Lee
Part III: Statistical inference
8. Discrete Graphical Models and their Parametrization - Luca La Rocca and Alberto Roverato
9. Gaussian Graphical Models - Caroline Uhler
10. Bayesian Inference in Graphical Gaussian Models - Hélène Massam
11. Latent Tree Models - Piotr Zwiernik
12.Neighborhood Selection Methods - Po-Ling Loh
12. Nonparametric Graphical Models - Han Liu and John Lafferty
14. Inference in High-Dimensional Graphical Models - Jana Janková and Sara van de Geer
Part IV: Causal inference
15. Causal Concepts and Graphical Models - Vanessa Didelez
16. Identication In Graphical Causal Models - Ilya Shpitser
17. Mediation Analysis - Johan Steen and Stijn Vansteelandt
18. Search for Causal Models - Peter Spirtes and Kun Zhang
Part V: Applications
19. Graphical Models for Forensic Analysis - A. Philip Dawid and Julia Mortera
20. Graphical Models in Molecular Systems Biology - Sach Mukherjee and Chris Oates
21. Graphical Models in Genetics, Genomics, and Metagenomics - Hongzhe Li and Jing Ma
"The Handbook of Graphical Models is an edited collection of chapters written by leading researchers and covering a wide range of topics on probabilistic graphical models. The editors, Marloes Maathuis, Mathias Drton, Steffen Lauritzen, and Martin Wainwright, are well-known statisticians and have conducted foundational research on graphical models. They have done a great job of soliciting and organizing chapters authored by top researchers from a variety of disciplines beyond just mathematics, probability and statistics; many authors hail from computer science, electrical engineering, economics, and even philosophy. It is precisely the multidisciplinary nature of this book that makes it stand out from other texts on graphical models. Because of this, the Handbook of Graphical Models will have broad appeal across many disciplines, providing a unique resource and excellent reference for those researching, studying, and using graphical models...Overall, the Handbook of Graphical Models is an important reference on probabilistic graphical models that will be used by researchers in statistics and probability, computer science, electrical engineering and beyond. The book stands out for its broad, multidisciplinary nature, with wide-ranging and largely theoretical coverage of core topics and the latest research on graphical models."
- Genevera I. Allen, JASA, August 2020