Learning the Stein Discrepancy for Training and Evaluating Energy-Based Models without Sampling

Will Grathwohl · Kuan-Chieh Wang · Joern-Henrik Jacobsen · David Duvenaud · Richard Zemel

Keywords: [ Deep Generative Models ] [ Generative Models ] [ Unsupervised and Semi-supervised Learning ] [ Probabilistic Inference - Models and Probabilistic Programming ]

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We present a new method for evaluating and training unnormalized density models. Our approach only requires access to the gradient of the unnormalized model’s log-density. We estimate the Stein discrepancy between the data density p(x) and the model density q(x) based on a vector function of the data. We parameterize this function with a neural network and fit its parameters to maximize this discrepancy. This yields a novel goodness-of-fit test which outperforms existing methods on high dimensional data. Furthermore, optimizing q(x) to minimize this discrepancy produces a novel method for training unnormalized models. This training method can fit large unnormalized models faster than existing approaches. The ability to both learn and compare models is a unique feature of the proposed method.

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