TSLiNGAM: DirectLiNGAM under heavy tails

TL;DR

TSLiNGAM is a new causal discovery method that improves robustness and efficiency in heavy-tailed and skewed data by leveraging non-Gaussian noise assumptions, outperforming existing algorithms.

Contribution

It introduces TSLiNGAM, an enhancement of DirectLiNGAM, specifically designed for heavy-tailed and skewed data, with theoretical justification and extensive empirical validation.

Findings

TSLiNGAM outperforms existing methods on heavy-tailed data.

It demonstrates high small-sample efficiency.

It is more resilient to data contamination.

Abstract

One of the established approaches to causal discovery consists of combining directed acyclic graphs (DAGs) with structural causal models (SCMs) to describe the functional dependencies of effects on their causes. Possible identifiability of SCMs given data depends on assumptions made on the noise variables and the functional classes in the SCM. For instance, in the LiNGAM model, the functional class is restricted to linear functions and the disturbances have to be non-Gaussian. In this work, we propose TSLiNGAM, a new method for identifying the DAG of a causal model based on observational data. TSLiNGAM builds on DirectLiNGAM, a popular algorithm which uses simple OLS regression for identifying causal directions between variables. TSLiNGAM leverages the non-Gaussianity assumption of the error terms in the LiNGAM model to obtain more efficient and robust estimation of the causal structure. TSLiNGAM is justified theoretically and is studied empirically in an extensive simulation study. It performs significantly better on heavy-tailed and skewed data and demonstrates a high small-sample efficiency. In addition, TSLiNGAM also shows better robustness properties as it is more resilient to contamination.