Inferring latent structure and causality is crucial for understanding underlying patterns and relationships hidden in the data. This book covers selected models for latent structures and causal networks and inference methods for these models.
After an introduction to the EM algorithm on incomplete data, the book provides a detailed coverage of a few widely used latent structure models, including mixture models, hidden Markov models, and stochastic block models. EM and variation EM algorithms are developed for parameter estimation under these models, with comparison to their Bayesian inference counterparts. We make further extensions of these models to related problems, such as clustering, motif discovery, Kalman filtering, and exchangeable random graphs. Conditional independence structures are utilized to infer the latent structures in the above models, which can be represented graphically. This notion generalizes naturally to the second part on graphical models that use graph separation to encode conditional independence. We cover a variety of graphical models, including undirected graphs, directed acyclic graphs (DAGs), chain graphs, and acyclic directed mixed graphs (ADMGs), and various Markov properties for these models. Recent methods that learn the structure of a graphical model from data are reviewed and discussed. In particular, DAGs and Bayesian networks are an important class of mathematical models for causality. After an introduction to causal inference with DAGs and structural equation models, we provide a detailed review of recent research on causal discovery via structure learning of graphs. Finally, we briefly introduce the causal bandit problem with sequential intervention.
Contents:
- Introduction and Review
- Latent Structure Models:
- Incomplete Data and the EM Algorithm
- Mixture Modeling
- Hidden Markov Models
- Random Graphs for Modeling Network Data
- Causal Graphical Models:
- Undirected Graphical Models
- Directed Acyclic Graphs
- Causal Inference Based on Directed Acyclic Graphs
- Structure Learning of Directed Acyclic Graphs
- Learning Generalized Directed Acyclic Graphical Models
- Directed Mixed Graphs for Latent Variables
- Partitioned, Federated, and Active Learning
Readership: This book is suitable for graduate students in statistics, data science, computer science and other quantitative and computational sciences. The book can be used as a textbook for courses on statistical modeling, causal inference, graphical models, and machine learning. It is also suitable for researchers interested in causal inference, causal discovery, graphical models, Bayesian networks, structure learning, latent structure models, and related areas.
Dr Qing Zhou is Professor of Statistics and Chair of the Department of Statistics and Data Science at the University of California, Los Angeles, USA. His research interests are in causal inference and graphical models, high-dimensional statistics, Monte Carlo methods, and bioinformatics. He holds a PhD in Statistics from Harvard University. Dr Zhou has published more than 50 research papers in statistics, machine learning, and computational biology. He has received a number of NSF research awards, including a Career award and a Big Data award.
'This is a very timely book for a systematic summary of the recent developments of network data analysis, graphical modeling, and causal inference.' - Faming Liang Distinguished Professor of Statistics Purdue University, USA
'This book covers an important set of topics that have not received as much exposure and would be a good addition to the literature.' - Vijay Nair Professor Emeritus University of Michigan, USA
