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

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) defined by a vector function of the data. We parameterize this function with a neural network and fit its parameters to maximize the 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 which scales more gracefully than existing methods. The ability to both learn and compare models is a unique feature of the proposed method.