A stochastic Stein Variational Newton method

• URL: http://arxiv.org/abs/2204.09039v1
• Date: Tue, 19 Apr 2022 17:57:36 GMT
• Title: A stochastic Stein Variational Newton method
• Authors: Alex Leviyev, Joshua Chen, Yifei Wang, Omar Ghattas, Aaron Zimmerman
• Abstract summary: We show that Stein variational Newton (sSVN) is a promising approach to accelerating high-precision Bayesian inference tasks. We demonstrate the effectiveness of our algorithm on a difficult class of test problems -- the Hybrid Rosenbrock density -- and show that sSVN converges using three orders of fewer magnitude evaluations of the log likelihood.
• Score: 7.272730677575111
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Stein variational gradient descent (SVGD) is a general-purpose optimization-based sampling algorithm that has recently exploded in popularity, but is limited by two issues: it is known to produce biased samples, and it can be slow to converge on complicated distributions. A recently proposed stochastic variant of SVGD (sSVGD) addresses the first issue, producing unbiased samples by incorporating a special noise into the SVGD dynamics such that asymptotic convergence is guaranteed. Meanwhile, Stein variational Newton (SVN), a Newton-like extension of SVGD, dramatically accelerates the convergence of SVGD by incorporating Hessian information into the dynamics, but also produces biased samples. In this paper we derive, and provide a practical implementation of, a stochastic variant of SVN (sSVN) which is both asymptotically correct and converges rapidly. We demonstrate the effectiveness of our algorithm on a difficult class of test problems -- the Hybrid Rosenbrock density -- and show that sSVN converges using three orders of magnitude fewer gradient evaluations of the log likelihood than its stochastic SVGD counterpart. Our results show that sSVN is a promising approach to accelerating high-precision Bayesian inference tasks with modest-dimension, $d\sim\mathcal{O}(10)$.

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