Statistical Causal Discovery: LiNGAM Approach

✍ Scribed by Shohei Shimizu

• Publisher: Springer
• Year: 2022
• Tongue: English
• Leaves: 99
• Series: SpringerBriefs in Statistics
• Category: Library

✦ Synopsis

This is the first book to provide a comprehensive introduction to a new semiparametric causal discovery approach known as LiNGAM, with the fundamental background needed to understand it. It offers a general overview of the basics of the LiNGAM approach for causal discovery, estimation principles, and algorithms.

This semiparametric approach is one of the most exciting new topics in the field of causal discovery. The new framework assumes parametric assumptions on the functional forms of structural equations but makes no assumption on the distributions of exogenous variables other than non-Gaussianity. It provides data-analysis tools capable of estimating a much wider class of causal relations even in the presence of hidden common causes. This feature is in contrast to conventional nonparametric approaches based on conditional independence of variables.

This book is highly recommended to readers who seek an in-depth and up-to-date overview of this new causal discovery approach to advance the technique as well as to those who are interested in applying this approach to real-world problems. This LiNGAM approach should become a standard item in the toolbox of statisticians, machine learners, and practitioners who need to perform observational studies.

✦ Table of Contents

Preface
Contents
Acronyms
1 Introduction
1.1 A Starting Point for Causal Inference
1.2 Framework of Causal Inference
1.3 Identification and Estimation of the Magnitude of Causation
1.4 Identification and Estimation of Causal Structures
1.5 Concluding Remarks
References
Part I Basics of LiNGAM Approach
2 Basic LiNGAM Model
2.1 Independent Component Analysis
2.2 LiNGAM Model
2.3 Identifiability of the LiNGAM model
2.4 Concluding Remarks
References
3 Estimation of the Basic LiNGAM Model
3.1 ICA-Based LiNGAM Algorithm
3.2 DirectLiNGAM Algorithm
3.3 Multigroup Analysis
3.3.1 LiNGAM Model for Multiple Groups
3.3.2 DirectLiNGAM Algorithm for Multiple LiNGAMs
3.4 Concluding Remarks
References
4 Evaluation of Statistical Reliability and Model Assumptions
4.1 Evaluation of Statistical Reliability
4.1.1 A Bootstrap Approach
4.1.2 Bootstrap Probability
4.1.3 Multiscale Bootstrap for LiNGAM
4.2 Evaluation of Model Assumptions
References
Part II Extended Models
5 LiNGAM with Hidden Common Causes
5.1 Identification and Estimation of Causal Structures of Confounded Variables
5.1.1 LiNGAM Model with Hidden Common Causes
5.1.2 Identification Based on Independent Component Analysis
5.1.3 Estimation Based on Independent Component Analysis
5.2 Identification and Estimation of Causal Structures of Unconfounded Variables
5.3 Other Hidden Variable Models
5.3.1 LiNGAM Model for Latent Factors
5.3.2 LiNGAM Model in the Presence of Latent Classes
References
6 Other Extensions
6.1 Cyclic Models
6.2 Time-Series Models
6.3 Nonlinear Models
6.4 Discrete Variable Models
References