Conditional Independence and Linear Programming

This book is the first to be devoted to the fusion between statistical causal inference and mathematical programming. The main purpose of the book is to provide the algorithms for solving the implication problem of conditional independence statements by using a computer. The concept of conditional independence is very much tied to the factorization of graphical models; hence it is very important to know the rules of conditional independence. Beginning with a brief introduction to linear programming, the book introduces the algebraic representations of conditional independence statements and their applications using linear programming methods. Through simple examples, it is shown that there are at least two different types of linear programming formulations for the implication problem. The first one is based on the concept of supermodular functions. Another is based on the fact that unnecessary information about the factorization of the probability distribution can be removed. This book also provides a detailed explanation of how to implement the solutions for the implication problem of conditional independence statements in R.