A Stein variational Newton method
Gianluca Detommaso, Tiangang Cui, Youssef Marzouk, Alessio Spantini, Robert Scheichl
Abstract
Stein variational gradient descent (SVGD) was recently proposed as a general purpose nonparametric variational inference algorithm: 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 [Liu & Wang, NIPS 2016]. 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.
BibTeX
@inproceedings{NEURIPS2018_fdaa09fc,
author = {Detommaso, Gianluca and Cui, Tiangang and Marzouk, Youssef and Spantini, Alessio and Scheichl, Robert},
booktitle = {Advances in Neural Information Processing Systems},
editor = {S. Bengio and H. Wallach and H. Larochelle and K. Grauman and N. Cesa-Bianchi and R. Garnett},
pages = {},
publisher = {Curran Associates, Inc.},
title = {A Stein variational Newton method},
url = {https://proceedings.neurips.cc/paper_files/paper/2018/file/fdaa09fc5ed18d3226b3a1a00f1bc48c-Paper.pdf},
volume = {31},
year = {2018}
}