On the Parameter Identifiability of Partially Observed Linear Causal Models

TL;DR

This paper investigates the parameter identifiability of partially observed linear causal models, providing theoretical conditions for identifiability, and proposes a likelihood-based estimation method validated on synthetic and real data.

Contribution

It extends prior work by allowing all variables to be related and considering all edge coefficients, offering new graphical conditions and a novel estimation approach.

Findings

Identifies three types of parameter indeterminacy.

Provides sufficient and necessary graphical conditions for identifiability.

Validates the method's effectiveness on synthetic and real datasets.

Abstract

Linear causal models are important tools for modeling causal dependencies and yet in practice, only a subset of the variables can be observed. In this paper, we examine the parameter identifiability of these models by investigating whether the edge coefficients can be recovered given the causal structure and partially observed data. Our setting is more general than that of prior research - we allow all variables, including both observed and latent ones, to be flexibly related, and we consider the coefficients of all edges, whereas most existing works focus only on the edges between observed variables. Theoretically, we identify three types of indeterminacy for the parameters in partially observed linear causal models. We then provide graphical conditions that are sufficient for all parameters to be identifiable and show that some of them are provably necessary. Methodologically, we propose a novel likelihood-based parameter estimation method that addresses the variance indeterminacy of latent variables in a specific way and can asymptotically recover the underlying parameters up to trivial indeterminacy. Empirical studies on both synthetic and real-world datasets validate our identifiability theory and the effectiveness of the proposed method in the finite-sample regime. Code: https://github.com/dongxinshuai/scm-identify.