Learning Measurement Models for Unobserved Variables

TL;DR

This paper presents a novel algorithm for discovering partitions of observed variables caused by unobserved latent variables, capable of inferring causal structures without prior knowledge of the number of latent factors.

Contribution

The introduced algorithm is asymptotically correct, does not require prior knowledge of latent variable count, and is applicable under standard causal Bayes net assumptions.

Findings

Algorithm accurately identifies latent variable partitions in simulated data.

It outperforms existing methods in scenarios with unknown number of latent variables.

The method is robust to different mathematical forms of latent relationships.

Abstract

Observed associations in a database may be due in whole or part to variations in unrecorded (latent) variables. Identifying such variables and their causal relationships with one another is a principal goal in many scientific and practical domains. Previous work shows that, given a partition of observed variables such that members of a class share only a single latent common cause, standard search algorithms for causal Bayes nets can infer structural relations between latent variables. We introduce an algorithm for discovering such partitions when they exist. Uniquely among available procedures, the algorithm is (asymptotically) correct under standard assumptions in causal Bayes net search algorithms, requires no prior knowledge of the number of latent variables, and does not depend on the mathematical form of the relationships among the latent variables. We evaluate the algorithm on a variety of simulated data sets.