Causal Discovery in the Presence of Measurement Error: Identifiability Conditions

TL;DR

This paper investigates the conditions under which causal models can be identified despite measurement errors, providing theoretical criteria based on statistical properties of the data.

Contribution

It introduces two sets of sufficient identifiability conditions for causal models with measurement error, leveraging second- and higher-order statistics.

Findings

Identifiability conditions based on second-order statistics.

Identifiability conditions based on higher-order statistics.

Clarifies what causal information can be recovered from contaminated data.

Abstract

Measurement error in the observed values of the variables can greatly change the output of various causal discovery methods. This problem has received much attention in multiple fields, but it is not clear to what extent the causal model for the measurement-error-free variables can be identified in the presence of measurement error with unknown variance. In this paper, we study precise sufficient identifiability conditions for the measurement-error-free causal model and show what information of the causal model can be recovered from observed data. In particular, we present two different sets of identifiability conditions, based on the second-order statistics and higher-order statistics of the data, respectively. The former was inspired by the relationship between the generating model of the measurement-error-contaminated data and the factor analysis model, and the latter makes use of the identifiability result of the over-complete independent component analysis problem.