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.

這本書是首次專注於統計因果推論和數學規劃之融合。該書的主要目的是提供使用電腦解決條件獨立性陳述的蘊含問題的演算法。條件獨立性的概念與圖形模型的因子化密切相關，因此了解條件獨立性的規則非常重要。從簡要介紹線性規劃開始，本書介紹了條件獨立性陳述的代數表示及其應用，並使用線性規劃方法進行求解。通過簡單的例子，書中展示了至少兩種不同類型的線性規劃形式來解決蘊含問題。第一種基於超模函數的概念，另一種則基於可以刪除概率分佈因子化的不必要信息的事實。本書還詳細解釋了如何在R中實現解決條件獨立性陳述的蘊含問題的解決方案。