Learning nonparametric DAGs with incremental information via high-order HSIC

TL;DR

This paper introduces a novel two-phase algorithm called OT for learning DAGs that leverages high-order HSIC to improve the identification of causal structures, outperforming existing methods in synthetic and real datasets.

Contribution

The paper proposes an identifiability condition and a two-phase OT algorithm that uses high-order HSIC for more accurate DAG structure learning.

Findings

OT algorithm achieves lower structure intervention distance (SID) than CAM.

OT outperforms existing methods on synthetic and real-world datasets.

High-order HSIC effectively guides local tuning of DAG structures.

Abstract

Score-based methods for learning Bayesain networks(BN) aim to maximizing the global score functions. However, if local variables have direct and indirect dependence simultaneously, the global optimization on score functions misses edges between variables with indirect dependent relationship, of which scores are smaller than those with direct dependent relationship. In this paper, we present an identifiability condition based on a determined subset of parents to identify the underlying DAG. By the identifiability condition, we develop a two-phase algorithm namely optimal-tuning (OT) algorithm to locally amend the global optimization. In the optimal phase, an optimization problem based on first-order Hilbert-Schmidt independence criterion (HSIC) gives an estimated skeleton as the initial determined parents subset. In the tuning phase, the skeleton is locally tuned by deletion, addition and DAG-formalization strategies using the theoretically proved incremental properties of high-order HSIC. Numerical experiments for different synthetic datasets and real-world datasets show that the OT algorithm outperforms existing methods. Especially in Sigmoid Mix model with the size of the graph being ${\rm\bf d=40}$, the structure intervention distance (SID) of the OT algorithm is 329.7 smaller than the one obtained by CAM, which indicates that the graph estimated by the OT algorithm misses fewer edges compared with CAM.Source code of the OT algorithm is available at https://github.com/YafeiannWang/optimal-tune-algorithm.