Causal Discovery via Quantile Partial Effect
This work addresses causal inference for researchers in statistics and machine learning, offering a method that generalizes previous identifiability results without relying on noise or Markov assumptions, though it is incremental in building on existing functional causal models.
The paper tackles the problem of causal discovery from observational data by introducing Quantile Partial Effect (QPE), a statistic based on conditional quantile regression, and shows that under certain assumptions, cause and effect are identifiable, with empirical validation on bivariate and multivariate datasets.
Quantile Partial Effect (QPE) is a statistic associated with conditional quantile regression, measuring the effect of covariates at different levels. Our theory demonstrates that when the QPE of cause on effect is assumed to lie in a finite linear span, cause and effect are identifiable from their observational distribution. This generalizes previous identifiability results based on Functional Causal Models (FCMs) with additive, heteroscedastic noise, etc. Meanwhile, since QPE resides entirely at the observational level, this parametric assumption does not require considering mechanisms, noise, or even the Markov assumption, but rather directly utilizes the asymmetry of shape characteristics in the observational distribution. By performing basis function tests on the estimated QPE, causal directions can be distinguished, which is empirically shown to be effective in experiments on a large number of bivariate causal discovery datasets. For multivariate causal discovery, leveraging the close connection between QPE and score functions, we find that Fisher Information is sufficient as a statistical measure to determine causal order when assumptions are made about the second moment of QPE. We validate the feasibility of using Fisher Information to identify causal order on multiple synthetic and real-world multivariate causal discovery datasets.