Quantifier Elimination for Statistical Problems

TL;DR

This paper explores the application of recent advances in quantifier elimination techniques to solve various complex problems in graphical models with hidden variables, including model comparison, identification, and constraint inference.

Contribution

It introduces a practical approach using improved Tarski's procedure for quantifier elimination to automatically solve problems in graphical models with hidden variables.

Findings

Feasible automatic solution for small instances of graphical model problems.

Effective comparison and analysis of models with hidden variables.

Quantifier elimination can determine model constraints and identifiability.

Abstract

Recent improvement on Tarski's procedure for quantifier elimination in the first order theory of real numbers makes it feasible to solve small instances of the following problems completely automatically: 1. listing all equality and inequality constraints implied by a graphical model with hidden variables. 2. Comparing graphyical models with hidden variables (i.e., model equivalence, inclusion, and overlap). 3. Answering questions about the identification of a model or portion of a model, and about bounds on quantities derived from a model. 4. Determing whether a given set of independence assertions. We discuss the foundation of quantifier elimination and demonstrate its application to these problems.