Choosing DAG Models Using Markov and Minimal Edge Count in the Absence of Ground Truth

TL;DR

This paper introduces a nonparametric test for DAG models and a search algorithm that rejects non-minimal models without ground truth, aiding causal structure learning from data.

Contribution

The paper presents the Markov Checker and CAFS algorithm, enabling model rejection and selection without ground truth, generalizing simplicity criteria for causal discovery.

Findings

CAFS can identify approximately correct models in simulations.

The Markov Checker provides a nonparametric test for the Markov condition.

The software tool handles large or dense models efficiently.

Abstract

We give a novel nonparametric pointwise consistent statistical test (the Markov Checker) of the Markov condition for directed acyclic graph (DAG) or completed partially directed acyclic graph (CPDAG) models given a dataset. We also introduce the Cross-Algorithm Frugality Search (CAFS) for rejecting DAG models that either do not pass the Markov Checker test or that are not edge minimal. Edge minimality has been used previously by Raskutti and Uhler as a nonparametric simplicity criterion, though CAFS readily generalizes to other simplicity conditions. Reference to the ground truth is not necessary for CAFS, so it is useful for finding causal structure learning algorithms and tuning parameter settings that output causal models that are approximately true from a given data set. We provide a software tool for this analysis that is suitable for even quite large or dense models, provided a suitably fast pointwise consistent test of conditional independence is available. In addition, we show in simulation that the CAFS procedure can pick approximately correct models without knowing the ground truth.