  Perturb-and-MAP offers an elegant approach to approximately sample from a
energy-based model (EBM) by computing the maximum-a-posteriori (MAP)
configuration of a perturbed version of the model. Sampling in turn enables
learning. However, this line of research has been hindered by the general
intractability of the MAP computation. Very few works venture outside tractable
models, and when they do, they use linear programming approaches, which as we
will show, have several limitations. In this work we present
perturb-and-max-product (PMP), a parallel and scalable mechanism for sampling
and learning in discrete EBMs. Models can be arbitrary as long as they are
built using tractable factors. We show that (a) for Ising models, PMP is orders
of magnitude faster than Gibbs and Gibbs-with-Gradients (GWG) at learning and
generating samples of similar or better quality; (b) PMP is able to learn and
sample from RBMs; (c) in a large, entangled graphical model in which Gibbs and
GWG fail to mix, PMP succeeds.
