A Stein variational Newton method
Machine Learning
2018-10-31 v2 Machine Learning
Numerical Analysis
Abstract
Stein variational gradient descent (SVGD) was recently proposed as a general purpose nonparametric variational inference algorithm [Liu & Wang, NIPS 2016]: it minimizes the Kullback-Leibler divergence between the target distribution and its approximation by implementing a form of functional gradient descent on a reproducing kernel Hilbert space. In this paper, we accelerate and generalize the SVGD algorithm by including second-order information, thereby approximating a Newton-like iteration in function space. We also show how second-order information can lead to more effective choices of kernel. We observe significant computational gains over the original SVGD algorithm in multiple test cases.
Cite
@article{arxiv.1806.03085,
title = {A Stein variational Newton method},
author = {Gianluca Detommaso and Tiangang Cui and Alessio Spantini and Youssef Marzouk and Robert Scheichl},
journal= {arXiv preprint arXiv:1806.03085},
year = {2018}
}
Comments
18 pages, 7 figures