Sparse Additive Model Pruning for Order-Based Causal Structure Learning

TL;DR

This paper introduces a fast, accurate pruning method for order-based causal structure learning using sparse additive models, improving efficiency over existing techniques without sacrificing accuracy.

Contribution

The paper proposes a novel sparse additive model-based pruning approach that bypasses hypothesis testing, enhancing computational efficiency and estimation accuracy in causal discovery.

Findings

Significantly faster pruning compared to existing methods.

Maintains or improves accuracy in causal structure estimation.

Effective on both synthetic and real datasets.

Abstract

Causal structure learning, also known as causal discovery, aims to estimate causal relationships between variables as a form of a causal directed acyclic graph (DAG) from observational data. One of the major frameworks is the order-based approach that first estimates a topological order of the underlying DAG and then prunes spurious edges from the fully-connected DAG induced by the estimated topological order. Previous studies often focus on the former ordering step because it can dramatically reduce the search space of DAGs. In practice, the latter pruning step is equally crucial for ensuring both computational efficiency and estimation accuracy. Most existing methods employ a pruning technique based on generalized additive models and hypothesis testing, commonly known as CAM-pruning. However, this approach can be a computational bottleneck as it requires repeatedly fitting additive models for all variables. Furthermore, it may harm estimation quality due to multiple testing. To address these issues, we introduce a new pruning method based on sparse additive models, which enables direct pruning of redundant edges without relying on hypothesis testing. We propose an efficient algorithm for learning sparse additive models by combining the randomized tree embedding technique with group-wise sparse regression. Experimental results on both synthetic and real datasets demonstrated that our method is significantly faster than existing pruning methods while maintaining comparable or superior accuracy.