  We revisit and generalize the concept of composite likelihood as a method to
make a probabilistic inference by aggregation of multiple Bayesian agents,
thereby defining a class of predictive models which we call composite Bayesian.
This perspective gives insight to choose the weights associated with composite
likelihood, either a priori or via learning; in the latter case, they may be
tuned so as to minimize prediction cross-entropy, yielding an easy-to-solve
convex problem. We argue that composite Bayesian inference is a middle way
between generative and discriminative models that trades off between
interpretability and prediction performance, both of which are crucial to many
artificial intelligence tasks.
