The Thermodynamic Variational Objective
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We introduce the thermodynamic variational objective (TVO) for learning in both continuous and discrete deep generative models. The TVO arises from a key connection between variational inference and thermodynamic integration that results in a tighter lower bound to the log marginal likelihood than the standard variational evidence lower bound (ELBO), while remaining as broadly applicable. We provide a computationally efficient gradient estimator for the TVO that applies to continuous, discrete, and non-reparameterizable distributions and show that the objective functions used in variational inference, variational autoencoders, wake sleep, and inference compilation are all special cases of the TVO. We evaluate the TVO for learning of discrete and continuous variational auto encoders, and find it achieves state of the art for learning in discrete variable models, and outperform VAEs on continuous variable models without using the reparameterization trick.
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