Likelihood-free hypothesis testing
Speaker: James Carzon
Abstract: Consider the problem of binary hypothesis testing Z ∼ P vs Z ∼ Q from m samples. Achieving a small error rate when P and Q are completely known is possible using the Neyman-Pearson test, for example. We consider a variation of the problem, which the authors call likelihood-free hypothesis testing, where access to P and Q (which are a priori only known to belong to a large non-parametric family) is given through iid samples from each. We discuss the minimax sample complexity of such a test, the proof of which borrows on the L^2 distance statistic of Ingster and the "Ingster trick." We discuss a fundamental trade-off between the size of the observed dataset Z and the size of the simulated datasets X ~ P and Y ~ Q.