Differentiable Causal Discovery For Latent Hierarchical Causal Models

TL;DR

This paper introduces a novel differentiable causal discovery method for nonlinear latent hierarchical models, overcoming previous limitations in scalability and assumptions, and demonstrating superior performance on high-dimensional data.

Contribution

It provides the first differentiable causal discovery algorithm for nonlinear latent hierarchical models, with new theoretical identifiability results and practical high-dimensional applications.

Findings

Outperforms existing methods in accuracy and scalability.

Successfully learns interpretable hierarchical latent structures from image data.

Effective on downstream tasks with high-dimensional data.

Abstract

Discovering causal structures with latent variables from observational data is a fundamental challenge in causal discovery. Existing methods often rely on constraint-based, iterative discrete searches, limiting their scalability to large numbers of variables. Moreover, these methods frequently assume linearity or invertibility, restricting their applicability to real-world scenarios. We present new theoretical results on the identifiability of nonlinear latent hierarchical causal models, relaxing previous assumptions in literature about the deterministic nature of latent variables and exogenous noise. Building on these insights, we develop a novel differentiable causal discovery algorithm that efficiently estimates the structure of such models. To the best of our knowledge, this is the first work to propose a differentiable causal discovery method for nonlinear latent hierarchical models. Our approach outperforms existing methods in both accuracy and scalability. We demonstrate its practical utility by learning interpretable hierarchical latent structures from high-dimensional image data and demonstrate its effectiveness on downstream tasks.