6 Supplementary Materials 6.1 Notation and Definitions Given a set X, we denote the set of probability measures on X

In cooperative inference, Y ang et al. ( 2018) defines a system of Since the teacher's hypothesis marginal and the learner's data marginal are always fixed, our alternating minimization scheme varies conditional probabilities: the hypothesis induced family of Note the other families of conditional probabilities and marginals can be found by Bayes' This is the first of the two equations that define cooperative inference at step one. The neural networks are randomly initialized. The results are listed in Table 1 . In this setting, Y ang et al. ( 2018) shows that the optimal communication plans for the teacher and learner are the same. Translated to our framework, Y ang et al. ( 2018) tells us that Figure 6.1: From left to right (a) model with alternating minimization on matrix In Figure 6.1 (a) and (b), we see that with alternating minimization, the mean of The neural network architectures are typical variational autoencoder architectures.