Reparametrization Invariance in non-parametric Causal Discovery

TL;DR

This paper introduces a reparametrization invariant method for non-parametric causal discovery that is robust to changes in marginal distributions, providing a more intrinsic assessment of causal relationships from observational data.

Contribution

It proposes a novel algorithm leveraging a non-parametric estimator that remains invariant under marginal distribution changes, enhancing causal inference robustness.

Findings

The method is competitive with existing causal discovery techniques.

It emphasizes uncertainty quantification in causal queries.

The approach is invariant to marginal distribution shifts.

Abstract

Causal discovery estimates the underlying physical process that generates the observed data: does X cause Y or does Y cause X? Current methodologies use structural conditions to turn the causal query into a statistical query, when only observational data is available. But what if these statistical queries are sensitive to causal invariants? This study investigates one such invariant: the causal relationship between X and Y is invariant to the marginal distributions of X and Y. We propose an algorithm that uses a non-parametric estimator that is robust to changes in the marginal distributions. This way we may marginalize the marginals, and inspect what relationship is intrinsically there. The resulting causal estimator is competitive with current methodologies and has high emphasis on the uncertainty in the causal query; an aspect just as important as the query itself.