Structure Learning for Directed Trees

TL;DR

This paper introduces a scalable, theoretically grounded method called causal additive trees (CAT) for learning directed tree causal structures from data, with proven consistency and effective hypothesis testing procedures.

Contribution

The paper proposes CAT, a fast algorithm for directed tree structure learning, with theoretical guarantees and new methods for hypothesis testing under uncertainty.

Findings

CAT outperforms existing methods in simulations

Proven consistency for Gaussian errors

Introduced hypothesis testing procedures with error control

Abstract

Knowing the causal structure of a system is of fundamental interest in many areas of science and can aid the design of prediction algorithms that work well under manipulations to the system. The causal structure becomes identifiable from the observational distribution under certain restrictions. To learn the structure from data, score-based methods evaluate different graphs according to the quality of their fits. However, for large, continuous, and nonlinear models, these rely on heuristic optimization approaches with no general guarantees of recovering the true causal structure. In this paper, we consider structure learning of directed trees. We propose a fast and scalable method based on Chu-Liu-Edmonds' algorithm we call causal additive trees (CAT). For the case of Gaussian errors, we prove consistency in an asymptotic regime with a vanishing identifiability gap. We also introduce two methods for testing substructure hypotheses with asymptotic family-wise error rate control that is valid post-selection and in unidentified settings. Furthermore, we study the identifiability gap, which quantifies how much better the true causal model fits the observational distribution, and prove that it is lower bounded by local properties of the causal model. Simulation studies demonstrate the favorable performance of CAT compared to competing structure learning methods.