Estimation of Structural Causal Model via Sparsely Mixing Independent Component Analysis

TL;DR

This paper introduces a new method for estimating sparse linear causal models from observational data by integrating ICA-based likelihood with penalties for sparsity, enabling simultaneous causal order and parameter estimation.

Contribution

It proposes a novel ICA-based estimation approach that incorporates sparsity penalties and improves efficiency over existing methods like LiNGAM and NOTEARS.

Findings

Outperforms existing methods in numerical experiments

Efficiently estimates causal order and parameters simultaneously

Demonstrates stability and effectiveness in sparse causal structure inference

Abstract

We consider the problem of inferring the causal structure from observational data, especially when the structure is sparse. This type of problem is usually formulated as an inference of a directed acyclic graph (DAG) model. The linear non-Gaussian acyclic model (LiNGAM) is one of the most successful DAG models, and various estimation methods have been developed. However, existing methods are not efficient for some reasons: (i) the sparse structure is not always incorporated in causal order estimation, and (ii) the whole information of the data is not used in parameter estimation. To address {these issues}, we propose a new estimation method for a linear DAG model with non-Gaussian noises. The proposed method is based on the log-likelihood of independent component analysis (ICA) with two penalty terms related to the sparsity and the consistency condition. The proposed method enables us to estimate the causal order and the parameters simultaneously. For stable and efficient optimization, we propose some devices, such as a modified natural gradient. Numerical experiments show that the proposed method outperforms existing methods, including LiNGAM and NOTEARS.