A Stein variational Newton method

Gianluca Detommaso; Tiangang Cui; Alessio Spantini; Youssef Marzouk; Robert Scheichl

A Stein variational Newton method

Gianluca Detommaso, Tiangang Cui, Alessio Spantini, Youssef Marzouk, Robert Scheichl

School of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research

8 Citations (Scopus)

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.

Original language	English
Title of host publication	Proceedings of Advances in Neural Information Processing Systems
Subtitle of host publication	32nd Conference on Neural Information Processing Systems, NeurIPS 2018; Montreal; Canada; 2 December 2018 through 8 December 2018
Editors	S Bengio, H Wallach, H Larochelle, K Grauman, N Cesa-Bianchi, R Garnett
Place of Publication	San Diego CA USA
Number of pages	11
Volume	2018-December
Publication status	Published - 1 Jan 2018
Event	Advances in Neural Information Processing Systems 2018 - Montreal Convention Center (Palais des Congrès de Montréal), Montreal , Canada Duration: 2 Dec 2018 → 8 Dec 2018 Conference number: 31st https://papers.nips.cc/book/advances-in-neural-information-processing-systems-31-2018 (Proceedings)

Publication series

Name	Advances in Neural Information Processing Systems
ISSN (Print)	1049-5258

Conference

Conference	Advances in Neural Information Processing Systems 2018
Abbreviated title	NIPS 2018
Country	Canada
City	Montreal
Period	2/12/18 → 8/12/18
Other	The Annual Conference on Neural Information Processing Systems (NeurIPS) is a multi-track machine learning and computational neuroscience conference that includes invited talks, demonstrations, symposia and oral and poster presentations of refereed papers. Following the conference, there are workshops which provide a less formal setting.
Internet address	https://papers.nips.cc/book/advances-in-neural-information-processing-systems-31-2018 (Proceedings)

Access to Document

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Cite this

Detommaso, G., Cui, T., Spantini, A., Marzouk, Y., & Scheichl, R. (2018). A Stein variational Newton method. In S. Bengio, H. Wallach, H. Larochelle, K. Grauman, N. Cesa-Bianchi, & R. Garnett (Eds.), Proceedings of Advances in Neural Information Processing Systems: 32nd Conference on Neural Information Processing Systems, NeurIPS 2018; Montreal; Canada; 2 December 2018 through 8 December 2018 (Vol. 2018-December). (Advances in Neural Information Processing Systems).. https://papers.nips.cc/paper/8130-a-stein-variational-newton-method

Detommaso, Gianluca ; Cui, Tiangang ; Spantini, Alessio ; Marzouk, Youssef ; Scheichl, Robert. / A Stein variational Newton method. Proceedings of Advances in Neural Information Processing Systems: 32nd Conference on Neural Information Processing Systems, NeurIPS 2018; Montreal; Canada; 2 December 2018 through 8 December 2018. editor / S Bengio ; H Wallach ; H Larochelle ; K Grauman ; N Cesa-Bianchi ; R Garnett. Vol. 2018-December San Diego CA USA, 2018. (Advances in Neural Information Processing Systems).

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title = "A Stein variational Newton method",

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.",

author = "Gianluca Detommaso and Tiangang Cui and Alessio Spantini and Youssef Marzouk and Robert Scheichl",

year = "2018",

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booktitle = "Proceedings of Advances in Neural Information Processing Systems",

note = "Advances in Neural Information Processing Systems 2018, NIPS 2018 ; Conference date: 02-12-2018 Through 08-12-2018",

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Detommaso, G, Cui, T, Spantini, A, Marzouk, Y & Scheichl, R 2018, A Stein variational Newton method. in S Bengio, H Wallach, H Larochelle, K Grauman, N Cesa-Bianchi & R Garnett (eds), Proceedings of Advances in Neural Information Processing Systems: 32nd Conference on Neural Information Processing Systems, NeurIPS 2018; Montreal; Canada; 2 December 2018 through 8 December 2018. vol. 2018-December, Advances in Neural Information Processing Systems, San Diego CA USA, Advances in Neural Information Processing Systems 2018, Montreal , Canada, 2/12/18. <https://papers.nips.cc/paper/8130-a-stein-variational-newton-method>

A Stein variational Newton method. / Detommaso, Gianluca; Cui, Tiangang; Spantini, Alessio; Marzouk, Youssef; Scheichl, Robert.

Proceedings of Advances in Neural Information Processing Systems: 32nd Conference on Neural Information Processing Systems, NeurIPS 2018; Montreal; Canada; 2 December 2018 through 8 December 2018. ed. / S Bengio; H Wallach; H Larochelle; K Grauman; N Cesa-Bianchi; R Garnett. Vol. 2018-December San Diego CA USA, 2018. (Advances in Neural Information Processing Systems).

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research

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N2 - 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.

AB - 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.

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Detommaso G, Cui T, Spantini A, Marzouk Y, Scheichl R. A Stein variational Newton method. In Bengio S, Wallach H, Larochelle H, Grauman K, Cesa-Bianchi N, Garnett R, editors, Proceedings of Advances in Neural Information Processing Systems: 32nd Conference on Neural Information Processing Systems, NeurIPS 2018; Montreal; Canada; 2 December 2018 through 8 December 2018. Vol. 2018-December. San Diego CA USA. 2018. (Advances in Neural Information Processing Systems).