Exponential Family Estimation via Adversarial Dynamics Embedding.

We present an efficient algorithm for maximum likelihood estimation (MLE) of the general exponential family, even in cases when the energy function is represented by a deep neural network. We consider the primal-dual view of the MLE for the kinectics augmented model, which naturally introduces an adversarial dual sampler. The sampler will be represented by a novel neural network architectures, dynamics embeddings, mimicking the dynamical-based samplers, e.g., Hamiltonian Monte-Carlo and its variants. The dynamics embedding parametrization inherits the flexibility from HMC, and provides tractable entropy estimation of the augmented model. Meanwhile, it couples the adversarial dual samplers with the primal model, reducing memory and sample complexity. We further show that several existing estimators, including contrastive divergence (Hinton, 2002), score matching (Hyvarinen, 2005), pseudo-likelihood (Besag, 1975), noise-contrastive estimation (Gutmann and Hyvarinen, 2010), non-local contrastive objectives (Vickrey et al., 2010), and minimum probability flow (Sohl-Dickstein et al., 2011), can be recast as the special cases of the proposed method with different prefixed dual samplers. Finally, we empirically demonstrate the superiority of the proposed estimator against existing state-of-the-art methods on synthetic and real-world benchmarks.