Learning Functional Causal Models with Generative Neural Networks

Olivier Goudet, Diviyan Kalainathan, Philippe Caillou, Isabelle Guyon, David Lopez-Paz, Michele Sebag

Abstract:

We introduce a new approach to functional causal modeling from observational data, called
Causal Generative Neural Networks (CGNN). CGNN leverages the power of neural networks
to learn a generative model of the joint distribution of the observed variables, by minimizing the
Maximum Mean Discrepancy between generated and observed data. An approximate learning
criterion is proposed to scale the computational cost of the approach to linear complexity in the
number of observations. The performance of CGNN is studied throughout three experiments.
Firstly, CGNN is applied to cause-effect inference, where the task is to identify the best causal
hypothesis out of “X → Y ” and “Y → X”. Secondly, CGNN is applied to the problem of iden-
tifying v-structures and conditional independences. Thirdly, CGNN is applied to multivariate
functional causal modeling: given a skeleton describing the direct dependences in a set of ran-
dom variables X = [X1, . . . , Xd ], CGNN orients the edges in the skeleton to uncover the directed
acyclic causal graph describing the causal structure of the random variables. On all three tasks,
CGNN is extensively assessed on both artificial and real-world data, comparing favorably to
the state-of-the-art. Finally, CGNN is extended to handle the case of confounders, where latent
variables are involved in the overall causal model.