Graph-based Discriminators: Sample Complexity and Expressiveness

A basic question in learning theory is to identify if two distributions are identical when we have access only to examples sampled from the distributions. This basic task is considered, for example, in the context of Generative Adversarial Networks (GANs), where a discriminator is trained to distinguish between a reallife distribution and a synthetic distribution. Classically, we use a hypothesis class H and claim that the two distributions are distinct if for some h H the expected value on the two distributions is (significantly) different. Our starting point is the following fundamental problem: "is having the hypothesis dependent on more than a single random example beneficial". To address this challenge we define k-ary based discriminators, which have a family of Boolean k-ary functions G.