  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.
