Finding Exogenous Variables in Data with Many More Variables than Observations

TL;DR

This paper introduces a new method for identifying exogenous variables in high-dimensional causal models, especially when the number of variables far exceeds the number of observations, using non-Gaussianity.

Contribution

The proposed approach efficiently finds exogenous variables in high-dimensional data without estimating the full causal structure, requiring smaller sample sizes.

Findings

Effective in p>>n scenarios with artificial data

Successfully applied to gene expression data

Outperforms traditional methods in high-dimensional settings

Abstract

Many statistical methods have been proposed to estimate causal models in classical situations with fewer variables than observations (p<n, p: the number of variables and n: the number of observations). However, modern datasets including gene expression data need high-dimensional causal modeling in challenging situations with orders of magnitude more variables than observations (p>>n). In this paper, we propose a method to find exogenous variables in a linear non-Gaussian causal model, which requires much smaller sample sizes than conventional methods and works even when p>>n. The key idea is to identify which variables are exogenous based on non-Gaussianity instead of estimating the entire structure of the model. Exogenous variables work as triggers that activate a causal chain in the model, and their identification leads to more efficient experimental designs and better understanding of the causal mechanism. We present experiments with artificial data and real-world gene expression data to evaluate the method.