Measuring Latent Causal Structure

TL;DR

This paper addresses the challenge of identifying and understanding the latent causal structure underlying observed data, especially when observed variables are influenced by multiple hidden causes, under linear assumptions.

Contribution

It extends existing methods for discovering latent causes to cases where observed variables are influenced by multiple latent variables, broadening applicability.

Findings

Extended methods to handle observed variables measuring multiple latent causes.

Provided theoretical conditions for identifiability of latent structure.

Demonstrated improved accuracy in latent cause discovery.

Abstract

Discovering latent representations of the observed world has become increasingly more relevant in data analysis. Much of the effort concentrates on building latent variables which can be used in prediction problems, such as classification and regression. A related goal of learning latent structure from data is that of identifying which hidden common causes generate the observations, such as in applications that require predicting the effect of policies. This will be the main problem tackled in our contribution: given a dataset of indicators assumed to be generated by unknown and unmeasured common causes, we wish to discover which hidden common causes are those, and how they generate our data. This is possible under the assumption that observed variables are linear functions of the latent causes with additive noise. Previous results in the literature present solutions for the case where each observed variable is a noisy function of a single latent variable. We show how to extend the existing results for some cases where observed variables measure more than one latent variable.