On Different Notions of Redundancy in Conditional-Independence-Based Discovery of Graphical Models
This work addresses the sensitivity of graphical model discovery algorithms to errors and assumptions, which is a problem for researchers and practitioners in statistics and machine learning, but it is incremental as it builds on existing methods.
The paper tackles the problem of unreliable statistical tests in conditional-independence-based discovery of graphical models by analyzing redundant tests, showing that some can detect or correct errors in learned models, while others are ineffective.
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.