Exponential Family Estimation via Adversarial Dynamics Embedding

Part of Advances in Neural Information Processing Systems 32 (NeurIPS 2019)

AuthorFeedback »Bibtex »Bibtex »MetaReview »Metadata »Paper »Reviews »Supplemental »

Authors

Bo Dai, Zhen Liu, Hanjun Dai, Niao He, Arthur Gretton, Le Song, Dale Schuurmans

Abstract

We present an efficient algorithm for maximum likelihood estimation (MLE) of exponential family models, with a general parametrization of the energy function that includes neural networks. We exploit the primal-dual view of the MLE with a kinetics augmented model to obtain an estimate associated with an adversarial dual sampler. To represent this sampler, we introduce a novel neural architecture, dynamics embedding, that generalizes Hamiltonian Monte-Carlo (HMC). The proposed approach inherits the flexibility of HMC while enabling tractable entropy estimation for the augmented model. By learning both a dual sampler and the primal model simultaneously, and sharing parameters between them, we obviate the requirement to design a separate sampling procedure once the model has been trained, leading to more effective learning. We show that many existing estimators, such as contrastive divergence, pseudo/composite-likelihood, score matching, minimum Stein discrepancy estimator, non-local contrastive objectives, noise-contrastive estimation, and minimum probability flow, are special cases of the proposed approach, each expressed by a different (fixed) dual sampler. An empirical investigation shows that adapting the sampler during MLE can significantly improve on state-of-the-art estimators.