Bayesian Discovery of Linear Acyclic Causal Models

TL;DR

This paper introduces a Bayesian score-based method for discovering linear acyclic causal models from non-Gaussian data, providing uncertainty quantification and improved accuracy over existing approaches.

Contribution

It develops a Bayesian approach that leverages non-Gaussianity in data to estimate causal models and express confidence levels, unlike previous methods that output only single graphs.

Findings

Bayesian method performs as well or better than existing methods on small networks.

The approach effectively utilizes non-Gaussianity for causal inference.

Complete R code package provided for implementation and analysis.

Abstract

Methods for automated discovery of causal relationships from non-interventional data have received much attention recently. A widely used and well understood model family is given by linear acyclic causal models (recursive structural equation models). For Gaussian data both constraint-based methods (Spirtes et al., 1993; Pearl, 2000) (which output a single equivalence class) and Bayesian score-based methods (Geiger and Heckerman, 1994) (which assign relative scores to the equivalence classes) are available. On the contrary, all current methods able to utilize non-Gaussianity in the data (Shimizu et al., 2006; Hoyer et al., 2008) always return only a single graph or a single equivalence class, and so are fundamentally unable to express the degree of certainty attached to that output. In this paper we develop a Bayesian score-based approach able to take advantage of non-Gaussianity when estimating linear acyclic causal models, and we empirically demonstrate that, at least on very modest size networks, its accuracy is as good as or better than existing methods. We provide a complete code package (in R) which implements all algorithms and performs all of the analysis provided in the paper, and hope that this will further the application of these methods to solving causal inference problems.