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.
Table of Contents
Part I Conditional independencies and Markov properties
Conditional Independence and Basic Markov Properties - Milan Studený
Markov Properties for Mixed Graphical Models - Robin Evans
Algebraic Aspects of Conditional Independence and Graphical Models - Thomas Kahle, Johannes Rauh, and Seth Sullivant
Part II Computing with factorizing distributions
Algorithms and Data Structures for Exact Computation of Marginals - Jeffrey A. Bilmes
Approximate methods for calculating marginals and likelihoods - Nicholas Ruozzi
MAP Estimation: Linear Programming Relaxation and Message-Passing Algorithms - Ofer Meshi and Alexander G. Schwing
Sequential Monte Carlo Methods - Arnaud Doucet and Anthony Lee
Part III Statistical inference
Discrete Graphical Models and their Parametrization - Luca La Rocca and Alberto Roverato
Gaussian Graphical Models - Caroline Uhler
Bayesian inference in Graphical Gaussian Models - Hélène Massam
Latent tree models - Piotr Zwiernik
Neighborhood selection methods - Po-Ling Loh
Nonparametric Graphical Models - Han Liu and John La□erty
Inference in high-dimensional graphical models - Jana Janková and Sara van de Geer
Part IV Causal inference
Causal Concepts and Graphical Models - Vanessa Didelez
Identi□cation In Graphical Causal Models - Ilya Shpitser
Mediation Analysis - Johan Steen and Stijn Vansteelandt
Search for Causal Models - Peter Spirtes and Kun Zhang
Part V Applications
Graphical Models for Forensic Analysis - A. Philip Dawid and Julia Mortera
Graphical models in molecular systems biology - Sach Mukherjee and Chris Oates
Graphical Models in Genetics, Genomics and Metagenomics - Hongzhe Li and Jing Ma
Marloes Maathuis is Professor of Statistics at ETH Zurich.
Mathias Drton is Professor of Statistics at the University of Copenhagen and the University of Washington.
Steffen Lauritzen is Professor of Statistics at the University of Copenhagen.
Martin Wainwright is Chancellor's Professor at the University of Berkeley.