Neural Causal Abstractions

TL;DR

This paper introduces a new family of neural causal abstractions based on clustering variables, enabling scalable causal inference in high-dimensional data like images, and integrates them with representation learning for practical applications.

Contribution

It develops a generalized clustering-based causal abstraction framework that is learnable with neural models and applicable to complex, high-dimensional data.

Findings

Effective in high-dimensional image data

Supports various causal inference tasks

Scalable with neural network methods

Abstract

The abilities of humans to understand the world in terms of cause and effect relationships, as well as to compress information into abstract concepts, are two hallmark features of human intelligence. These two topics have been studied in tandem in the literature under the rubric of causal abstractions theory. In practice, it remains an open problem how to best leverage abstraction theory in real-world causal inference tasks, where the true mechanisms are unknown and only limited data is available. In this paper, we develop a new family of causal abstractions by clustering variables and their domains. This approach refines and generalizes previous notions of abstractions to better accommodate individual causal distributions that are spawned by Pearl's causal hierarchy. We show that such abstractions are learnable in practical settings through Neural Causal Models (Xia et al., 2021), enabling the use of the deep learning toolkit to solve various challenging causal inference tasks -- identification, estimation, sampling -- at different levels of granularity. Finally, we integrate these results with representation learning to create more flexible abstractions, moving these results closer to practical applications. Our experiments support the theory and illustrate how to scale causal inferences to high-dimensional settings involving image data.