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Variational Sequential Monte Carlo
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
Columbia University, New York City, New York, United States.
New York University, New York City, New York, United States.
Columbia University, New York City, New York, United States.
2018 (English)In: Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, 2018Conference paper, Published paper (Refereed)
Abstract [en]

Many recent advances in large scale probabilistic inference rely on variational methods. The success of variational approaches depends on (i) formulating a flexible parametric family of distributions, and (ii) optimizing the parameters to find the member of this family that most closely approximates the exact posterior. In this paper we present a new approximating family of distributions, the variational sequential Monte Carlo (VSMC) family, and show how to optimize it in variational inference. VSMC melds variational inference (VI) and sequential Monte Carlo (SMC), providing practitioners with flexible, accurate, and powerful Bayesian inference. The VSMC family is a variational family that can approximate the posterior arbitrarily well, while still allowing for efficient optimization of its parameters. We demonstrate its utility on state space models, stochastic volatility models for financial data, and deep Markov models of brain neural circuits.

Place, publisher, year, edition, pages
2018.
National Category
Computer Sciences
Identifiers
URN: urn:nbn:se:liu:diva-152646OAI: oai:DiVA.org:liu-152646DiVA, id: diva2:1262051
Conference
International Conference on Artificial Intelligence and Statistics, Playa Blanca, Lanzarote, Canary Islands, April 9 - 11, 2018
Available from: 2018-11-09 Created: 2018-11-09 Last updated: 2018-11-16Bibliographically approved
In thesis
1. Machine learning using approximate inference: Variational and sequential Monte Carlo methods
Open this publication in new window or tab >>Machine learning using approximate inference: Variational and sequential Monte Carlo methods
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Automatic decision making and pattern recognition under uncertainty are difficult tasks that are ubiquitous in our everyday life. The systems we design, and technology we develop, requires us to coherently represent and work with uncertainty in data. Probabilistic models and probabilistic inference gives us a powerful framework for solving this problem. Using this framework, while enticing, results in difficult-to-compute integrals and probabilities when conditioning on the observed data. This means we have a need for approximate inference, methods that solves the problem approximately using a systematic approach. In this thesis we develop new methods for efficient approximate inference in probabilistic models.

There are generally two approaches to approximate inference, variational methods and Monte Carlo methods. In Monte Carlo methods we use a large number of random samples to approximate the integral of interest. With variational methods, on the other hand, we turn the integration problem into that of an optimization problem. We develop algorithms of both types and bridge the gap between them.

First, we present a self-contained tutorial to the popular sequential Monte Carlo (SMC) class of methods. Next, we propose new algorithms and applications based on SMC for approximate inference in probabilistic graphical models. We derive nested sequential Monte Carlo, a new algorithm particularly well suited for inference in a large class of high-dimensional probabilistic models. Then, inspired by similar ideas we derive interacting particle Markov chain Monte Carlo to make use of parallelization to speed up approximate inference for universal probabilistic programming languages. After that, we show how we can make use of the rejection sampling process when generating gamma distributed random variables to speed up variational inference. Finally, we bridge the gap between SMC and variational methods by developing variational sequential Monte Carlo, a new flexible family of variational approximations.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2018. p. 39
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1969
National Category
Control Engineering Computer Sciences Signal Processing
Identifiers
urn:nbn:se:liu:diva-152647 (URN)10.3384/diss.diva-152647 (DOI)9789176851616 (ISBN)
Public defence
2018-12-14, Ada Lovelace, Building B, Campus Valla, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2018-11-27 Created: 2018-11-09 Last updated: 2018-12-05Bibliographically approved

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