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On particle-based online smoothing and parameter inference in general hidden Markov models
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0001-9565-7686
2015 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of two papers studying online inference in general hidden Markov models using sequential Monte Carlo methods.

The first paper present an novel algorithm, the particle-based, rapid incremental smoother (PaRIS), aimed at efficiently perform online approximation of smoothed expectations of additive state functionals in general hidden Markov models. The algorithm has, under weak assumptions, linear computational complexity and very limited memory requirements. The algorithm is also furnished with a number of convergence results, including a central limit theorem.

The second paper focuses on the problem of online estimation of parameters in a general hidden Markov model. The algorithm is based on a forward implementation of the classical expectation-maximization algorithm. The algorithm uses the PaRIS algorithm to achieve an efficient algorithm.

Abstract [sv]

Denna avhandling består av två artiklar som behandlar inferens i dolda Markovkedjor med generellt tillståndsrum via sekventiella Monte Carlo-metoder.

Den första artikeln presenterar en ny algoritm, PaRIS, med målet att effektivt beräkna partikelbaserade online-skattningar av utjämnade väntevärden av additiva tillståndsfunktionaler. Algoritmen har, under svaga villkor, en beräkningkomplexitet som växer endast linjärt med antalet partiklar samt h\ögst begränsade minneskrav. Dessutom härleds ett antal konvergensresultat för denna algoritm, såsom en central gränsvärdessats.

Den andra artikeln fokuserar på online-estimering av modellparametrar i en generella dolda Markovkedjor. Den presenterade algoritmen kan ses som en kombination av PaRIS och en nyligen föreslagen online-implementation av den klassiska EM-algoritmen.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2015. , viii, 15 p.
Series
TRITA-MAT-A, 2015:06
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-166629ISBN: 978-91-7595-554-4 (print)OAI: oai:DiVA.org:kth-166629DiVA: diva2:811884
Presentation
2015-06-05, Rum 3721, Institutionen för matematik, Lindstedtsvägen 25, KTH, Stockholm, 14:00 (English)
Opponent
Supervisors
Note

QC 20150521

Available from: 2015-05-21 Created: 2015-05-12 Last updated: 2015-05-21Bibliographically approved
List of papers
1. Efficient particle-based online smoothing in general hidden Markov models: the PaRIS algorithm
Open this publication in new window or tab >>Efficient particle-based online smoothing in general hidden Markov models: the PaRIS algorithm
(English)Manuscript (preprint) (Other academic)
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:kth:diva-166617 (URN)
Note

QS 2015

Available from: 2015-05-12 Created: 2015-05-12 Last updated: 2015-05-21Bibliographically approved
2. An efficient particle-based online EM algorithm for general state-space models
Open this publication in new window or tab >>An efficient particle-based online EM algorithm for general state-space models
(English)Manuscript (preprint) (Other academic)
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:kth:diva-166628 (URN)
Note

QS 2015

Available from: 2015-05-12 Created: 2015-05-12 Last updated: 2015-05-21Bibliographically approved

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Licentiate Thesis(303 kB)166 downloads
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