WC(S) condition P0 densities, approximation bounding 5.3 Using Herewe parametrized H inpractice. exponential basemeasure, f(t)= Z 1f(t)= PI i=1 ik(t, ti) and B for functionV(t)= B (t). Unlikf is f inan RKHS, normalizing Z = R Sexp2 ( f(t))dQvia toobtainp(t).

Subsequently,wedefineequivariant energy based models to model invariant densities that are learned using contrastivedivergence.

Machine learning systems deployed in the real-world interact with people through their decision making.

Machine learned models are increasingly entering wider ranges ofdomains inour lives, driving a constantly increasing number of important systems. Large scale systems can be trained in highly parallel and distributed training environments, with a large amount of randomness in training the models.

WhenthefunctionF is convex, thisisalsoknownas Stochastic Convex Optimization (SCO).