Constraint-Based Causal Discovery: Conflict Resolution with Answer Set Programming

Abstract

Recent approaches to causal discovery based on Boolean satisfiability solvers have opened new opportunities to consider search spaces for causal models with both feedback cycles and unmea-sured confounders. However, the available meth-ods have so far not been able to provide a prin-cipled account of how to handle conflicting con-straints that arise from statistical variability. Here we present a new approach that preserves the ver-satility of Boolean constraint solving and attains a high accuracy despite the presence of statisti-cal errors. We develop a new logical encoding of (in)dependence constraints that is both well suited for the domain and allows for faster solv-ing. We represent this encoding in Answer Set Programming (ASP), and apply a state-of-the-art ASP solver for the optimization task. Based on different theoretical motivations, we explore a variety of methods to handle statistical errors. Our approach currently scales to cyclic latent variable models with up to seven observed vari-ables and outperforms the available constraint-based methods in accuracy. 1