Statistical Inference for Generative Models with Maximum Mean Discrepancy

Understand

While likelihood-based inference and its variants provide a statistically efficient and widely applicable approach to parametric inference, their application to models involving intractable likelihoods poses challenges.

• In this work, we study a class of minimum distance estimators for intractable generative models, that is, statistical models for which the likelihood is intractable, but simulation is cheap.
• The distance considered, maximum mean discrepancy (MMD), is defined through the embedding of probability measures into a reproducing kernel Hilbert space.
• We study the theoretical properties of these estimators, showing that they are consistent, asymptotically normal and robust to model misspecification.