On Different Notions of Redundancy in Conditional-Independence-Based Discovery of Graphical Models

TL;DR

This paper examines the role of redundant conditional independence tests in graphical model discovery, highlighting their potential to detect errors but also their limitations.

Contribution

It clarifies which types of tests can effectively detect or correct errors in learned graphical models, emphasizing the importance of test selection.

Findings

Redundant tests can sometimes detect or correct errors in models.

Not all tests provide additional useful information; some are less effective.

Tests based on graphical assumptions are more likely to detect errors.

Abstract

Conditional-independence-based discovery uses statistical tests to identify a graphical model that represents the independence structure of variables in a dataset. These tests, however, can be unreliable, and algorithms are sensitive to errors and violated assumptions. Often, there are tests that were not used in the construction of the graph. In this work, we show that these redundant tests have the potential to detect or sometimes correct errors in the learned model. But we further show that not all tests contain this additional information and that such redundant tests have to be applied with care. Precisely, we argue that the conditional (in)dependence statements that hold for every probability distribution are unlikely to detect and correct errors - in contrast to those that follow only from graphical assumptions.