Score-based Causal Representation Learning with Interventions

TL;DR

This paper introduces a method for causal representation learning that leverages score functions and interventions to recover latent causal structures and transformations, even with unknown linear mappings and various intervention types.

Contribution

It provides sufficient conditions for DAG recovery from interventions and demonstrates how score variations enable the identification of latent causal structures and transformations.

Findings

Sufficient conditions for DAG recovery are established.

Score functions' variations are key to identifying causal effects.

Method works with soft and hard interventions under certain assumptions.

Abstract

This paper studies the causal representation learning problem when the latent causal variables are observed indirectly through an unknown linear transformation. The objectives are: (i) recovering the unknown linear transformation (up to scaling) and (ii) determining the directed acyclic graph (DAG) underlying the latent variables. Sufficient conditions for DAG recovery are established, and it is shown that a large class of non-linear models in the latent space (e.g., causal mechanisms parameterized by two-layer neural networks) satisfy these conditions. These sufficient conditions ensure that the effect of an intervention can be detected correctly from changes in the score. Capitalizing on this property, recovering a valid transformation is facilitated by the following key property: any valid transformation renders latent variables' score function to necessarily have the minimal variations across different interventional environments. This property is leveraged for perfect recovery of the latent DAG structure using only \emph{soft} interventions. For the special case of stochastic \emph{hard} interventions, with an additional hypothesis testing step, one can also uniquely recover the linear transformation up to scaling and a valid causal ordering.