Moment Matters: Mean and Variance Causal Graph Discovery from Heteroscedastic Data

Yoichi Chikahara

Keywords: causal discovery; structural causal models; heteroscedastic noise models

TL;DR: We propose a moment-driven causal discovery framework that can identify the cause variables that affect the mean and those that influence the variance, leading to a better understanding of complex real-world phenomena.

Abstract:

This paper proposes a Bayesian causal discovery approach
to uncover the causal mechanisms
underlying heteroscedasticity,
where the variance of one variable is influenced
by the values of the others.
To distinguish between the causes that affect the mean
and those that influence the variance,
we infer the posterior distribution over
*mean* and *variance causal graphs*,
whose structures can be different,
depending on the moment information.
We establish identifiability conditions for these causal graphs
by extending the results on heteroscedastic noise models (HNMs).
Building on these conditions,
we develop a variational inference framework that can
incorporate prior knowledge about
the node orderings of the underlying graphs.
We experimentally show that our method can successfully infer both mean and variance causal graphs,
outperforming the state-of-the-art baselines.

Primary Area: causal reasoning

Submission Number: 11873