A probabilistic autoencoder for causal discovery

The paper addresses the problem of finding the causal direction between two associated variables. The proposed solution is to build an autoencoder of their joint distribution and to maximize its estimation capacity relative to both the marginal distributions. It is shown that the resulting two capacities cannot, in general, be equal. This leads to a new criterion for causal discovery: the higher capacity is consistent with the unconstrained choice of a distribution representing the cause while the lower capacity reflects the constraints imposed by the mechanism on the distribution of the effect. Estimation capacity is defined as the ability of the auto-encoder to represent arbitrary datasets. A regularization term forces it to decide which one of the variables to model in a more generic way i.e., while maintaining higher model capacity. The causal direction is revealed by the constraints encountered while encoding the data instead of being measured as a property of the data itself. The idea is implemented and tested using a restricted Boltzmann machine.