Reparametrization Invariance in non-parametric Causal Discovery
This work addresses the challenge of ensuring causal discovery methods are invariant to marginal distribution changes, which is important for researchers and practitioners in fields like statistics and machine learning, though it appears incremental as it builds on existing methodologies.
The paper tackles the problem of causal discovery from observational data by proposing a non-parametric estimator that is robust to changes in marginal distributions, ensuring invariance to causal invariants. The resulting causal estimator is competitive with current methodologies and emphasizes uncertainty in causal queries.
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.