Title: Moment Matters: Mean and Variance Causal Graph Discovery from Heteroscedastic Data
Primary area: causal reasoning
Keywords: causal discovery; structural causal models; heteroscedastic noise models

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.

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.