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Accelerated Stein Variational Gradient Flow
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DOI：10.1007/978-3-032-03921-7_9.png)
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Abstract
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Stein variational gradient descent (SVGD) is a kernel-based particle method for sampling from a target distribution, e.g., in Bayesian inference. SVGD does not require estimating the gradient of the log-density, which is called score estimation. In practice, SVGD can be slow compared to score-estimation-based sampling algorithms. To design fast and efficient high-dimensional sampling algorithms, we introduce ASVGD, an accelerated SVGD, based on an accelerated gradient flow in a metric space of probability densities following Nesterov's method. We then derive a momentum-based discrete-time sampling algorithm, which evolves a set of particles deterministically. To stabilize the particles position update, we also study a Wasserstein metric regularization. For the generalized bilinear kernel and the Gaussian kernel, toy numerical examples with varied target distributions demonstrate the effectiveness of ASVGD compared to SVGD and other popular sampling methods.
Keywords:
Nesterov's accelerated gradient method
Information geometry
Kernel methods
Score functions
Interacting particle system
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