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Machine learning using approximate inference: Variational and sequential Monte Carlo methods
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
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: urn:nbn:se:liu:diva-152647DOI: 10.3384/diss.diva-152647ISBN: 9789176851616 (print)OAI: oai:DiVA.org:liu-152647DiVA, id: diva2:1262062
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
List of papers
1. Capacity estimation of two-dimensional channels using Sequential Monte Carlo
Open this publication in new window or tab >>Capacity estimation of two-dimensional channels using Sequential Monte Carlo
2014 (English)In: 2014 IEEE Information Theory Workshop, 2014, p. 431-435Conference paper, Published paper (Refereed)
Abstract [en]

We derive a new Sequential-Monte-Carlo-based algorithm to estimate the capacity of two-dimensional channel models. The focus is on computing the noiseless capacity of the 2-D (1, ∞) run-length limited constrained channel, but the underlying idea is generally applicable. The proposed algorithm is profiled against a state-of-the-art method, yielding more than an order of magnitude improvement in estimation accuracy for a given computation time.

National Category
Control Engineering Computer Sciences Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-112966 (URN)10.1109/ITW.2014.6970868 (DOI)
Conference
Information Theory Workshop
Available from: 2015-01-06 Created: 2015-01-06 Last updated: 2018-11-09
2. Sequential Monte Carlo for Graphical Models
Open this publication in new window or tab >>Sequential Monte Carlo for Graphical Models
2014 (English)In: Advances in Neural Information Processing Systems, 2014, p. 1862-1870Conference paper, Published paper (Refereed)
Abstract [en]

We propose a new framework for how to use sequential Monte Carlo (SMC) algorithms for inference in probabilistic graphical models (PGM). Via a sequential decomposition of the PGM we find a sequence of auxiliary distributions defined on a monotonically increasing sequence of probability spaces. By targeting these auxiliary distributions using SMC we are able to approximate the full joint distribution defined by the PGM. One of the key merits of the SMC sampler is that it provides an unbiased estimate of the partition function of the model. We also show how it can be used within a particle Markov chain Monte Carlo framework in order to construct high-dimensional block-sampling algorithms for general PGMs.

National Category
Computer Sciences Probability Theory and Statistics Control Engineering
Identifiers
urn:nbn:se:liu:diva-112967 (URN)
Conference
Neural Information Processing Systems (NIPS)
Available from: 2015-01-06 Created: 2015-01-06 Last updated: 2018-11-09Bibliographically approved
3. Nested Sequential Monte Carlo Methods
Open this publication in new window or tab >>Nested Sequential Monte Carlo Methods
2015 (English)In: Proceedings of The 32nd International Conference on Machine Learning / [ed] Francis Bach, David Blei, Journal of Machine Learning Research (Online) , 2015, Vol. 37, p. 1292-1301Conference paper, Published paper (Refereed)
Abstract [en]

We propose nested sequential Monte Carlo (NSMC), a methodology to sample from sequences of probability distributions, even where the random variables are high-dimensional. NSMC generalises the SMC framework by requiring only approximate, properly weighted, samples from the SMC proposal distribution, while still resulting in a correct SMC algorithm. Furthermore, NSMC can in itself be used to produce such properly weighted samples. Consequently, one NSMC sampler can be used to construct an efficient high-dimensional proposal distribution for another NSMC sampler, and this nesting of the algorithm can be done to an arbitrary degree. This allows us to consider complex and high-dimensional models using SMC. We show results that motivate the efficacy of our approach on several filtering problems with dimensions in the order of 100 to 1 000.

Place, publisher, year, edition, pages
Journal of Machine Learning Research (Online), 2015
Series
JMLR Workshop and Conference Proceedings, ISSN 1938-7228 ; 37
National Category
Computer Sciences Control Engineering Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-122698 (URN)
Conference
32nd International Conference on Machine Learning, Lille, France, 6-11 July, 2015
Available from: 2015-11-16 Created: 2015-11-16 Last updated: 2018-11-09Bibliographically approved
4. Interacting Particle Markov Chain Monte Carlo
Open this publication in new window or tab >>Interacting Particle Markov Chain Monte Carlo
Show others...
2016 (English)In: Proceedings of the 33rd International Conference on Machine Learning (ICML), 2016Conference paper, Published paper (Refereed)
Abstract [en]

We introduce interacting particle Markov chain Monte Carlo (iPMCMC), a PMCMC method based on an interacting pool of standard and conditional sequential Monte Carlo samplers. Like related methods, iPMCMC is a Markov chain Monte Carlo sampler on an extended space. We present empirical results that show significant improvements in mixing rates relative to both non-interacting PMCMC samplers and a single PMCMC sampler with an equivalent memory and computational budget. An additional advantage of the iPMCMC method is that it is suitable for distributed and multi-core architectures.

Keywords
Sequential Monte Carlo, Probabilistic programming, parallelisation
National Category
Computer Sciences Control Engineering Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-130043 (URN)
Conference
International Conference on Machine Learning (ICML), New York, USA, June 19-24, 2016
Projects
CADICS
Funder
Cancer and Allergy Foundation
Available from: 2016-07-05 Created: 2016-07-05 Last updated: 2018-11-09
5. Reparameterization Gradients through Acceptance-Rejection Sampling Algorithms
Open this publication in new window or tab >>Reparameterization Gradients through Acceptance-Rejection Sampling Algorithms
2017 (English)In: Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, 2017Conference paper, Published paper (Refereed)
Abstract [en]

Variational inference using the reparameterization trick has enabled large-scale approximate Bayesian inference in complex probabilistic models, leveraging stochastic optimization to sidestep intractable expectations. The reparameterization trick is applicable when we can simulate a random variable by applying a differentiable deterministic function on an auxiliary random variable whose distribution is fixed. For many distributions of interest (such as the gamma or Dirichlet), simulation of random variables relies on acceptance-rejection sampling. The discontinuity introduced by the accept-reject step means that standard reparameterization tricks are not applicable. We propose a new method that lets us leverage reparameterization gradients even when variables are outputs of a acceptance-rejection sampling algorithm. Our approach enables reparameterization on a larger class of variational distributions. In several studies of real and synthetic data, we show that the variance of the estimator of the gradient is significantly lower than other state-of-the-art methods. This leads to faster convergence of stochastic gradient variational inference.

Series
Proceedings of Machine Learning Research, ISSN 1938-7228 ; 54
National Category
Computer Sciences
Identifiers
urn:nbn:se:liu:diva-152645 (URN)
Conference
Artificial Intelligence and Statistics, 20-22 April 2017, Fort Lauderdale, FL, USA
Available from: 2018-11-09 Created: 2018-11-09 Last updated: 2018-11-21
6. Variational Sequential Monte Carlo
Open this publication in new window or tab >>Variational Sequential Monte Carlo
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.

National Category
Computer Sciences
Identifiers
urn:nbn:se:liu:diva-152646 (URN)
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

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Andersson Naesseth, Christian

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