Conditional Independence and Linear Programming

This book is the first to combine statistical causal inference and mathematical programming to solve the implication problem of conditional independence statements. It introduces linear programming methods to represent and solve conditional independence statements, with two different formulations based on supermodular functions and information removal. It also provides instructions for implementing the solutions in R.

Format: Paperback / softback
Length: 46 pages
Publication date: 21 February 2024
Publisher: Springer Verlag, Japan

This groundbreaking book is a pioneering exploration of the fusion between statistical causal inference and mathematical programming. Its primary objective is to offer comprehensive algorithms for solving the implication problem of conditional independence statements through the utilization of computer technology. Conditional independence plays a pivotal role in the factorization of graphical models, making it essential to understand its principles. The book begins with a concise introduction to linear programming, laying the foundation for subsequent discussions. It then delves into the algebraic representations of conditional independence statements and their practical applications using linear programming methodologies. Through illustrative examples, the book demonstrates that the implication problem can be approached in at least two distinct linear programming formulations. The first formulation relies on the concept of supermodular functions, while the second leverages the fact that unnecessary information about the factorization of the probability distribution can be discarded. Furthermore, the book provides a detailed explanation of how to implement the solutions for the implication problem of conditional independence statements in the widely-used programming language R. By offering a comprehensive and practical approach, this book empowers researchers and practitioners to leverage the power of mathematical programming and statistical causal inference in addressing complex real-world problems.

Dimension: 235 x 155 (mm)
ISBN-13: 9784431552789
Edition number: 1st ed. 2024