Stein variational gradient descent (SVGD) is a particle-based inference algorithm that leverages gradient information for efficient approximate inference. In this work, we enhance SVGD by leveraging preconditioning matrices, such as the Hessian and Fisher information matrix, to incorporate geometric information into SVGD updates. We achieve this by presenting a generalization of SVGD that replaces the scalar-valued kernels in vanilla SVGD with more general matrix-valued kernels. This yields a significant extension of SVGD, and more importantly, allows us to flexibly incorporate various preconditioning matrices to accelerate the exploration in the probability landscape. Empirical results show that our method outperforms vanilla SVGD and a variety of baseline approaches over a range of real-world Bayesian inference tasks.
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Stein Variational Inference for Discrete Distributions
Gradient-based approximate inference methods, such as Stein variational gradient descent (SVGD), provide simple and general-purpose inference engines for differentiable continuous distributions. However, existing forms of SVGD cannot be directly applied to discrete distributions. In this work, we fill this gap by proposing a simple yet general framework that transforms discrete distributions to equivalent piecewise continuous distributions, on which the gradient-free SVGD is applied to perform efficient approximate inference. The empirical results show that our method outperforms traditional algorithms such as Gibbs sampling and discontinuous Hamiltonian Monte Carlo on various challenging benchmarks of discrete graphical models. We demonstrate that our method provides a promising tool for learning ensembles of binarized neural network (BNN), outperforming other widely used ensemble methods on learning binarized AlexNet on CIFAR-10 dataset. In addition, such transform can be straightforwardly employed in gradient-free kernelized Stein discrepancy to perform goodness-of-fit (GOF) test on discrete distributions. Our proposed method outperforms existing GOF test methods for intractable discrete distributions.
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- Award ID(s):
- 1846421
- NSF-PAR ID:
- 10172993
- Date Published:
- Journal Name:
- International Conference on Artificial Intelligence and Statistics
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
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