Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Particle-based, online estimation of tangent filters with application to parameter estimation in nonlinear state-space models
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.ORCID iD: 0000-0001-9565-7686
(English)Manuscript (preprint) (Other academic)
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-215291OAI: oai:DiVA.org:kth-215291DiVA, id: diva2:1147561
Note

QC 20171009

Available from: 2017-10-06 Created: 2017-10-06 Last updated: 2017-10-09Bibliographically approved
In thesis
1. On particle-based online smoothing and parameter inference in general state-space models
Open this publication in new window or tab >>On particle-based online smoothing and parameter inference in general state-space models
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of 4 papers, presented in Paper A-D, on particle- based online smoothing and parameter inference in general state-space hidden Markov models.

In Paper A a novel algorithm, the particle-based, rapid incremental smoother (PaRIS), aimed at efficiently performing online approxima- tion of smoothed expectations of additive state functionals in general hidden Markov models, is presented. The algorithm has, under weak assumptions, linear computational complexity and very limited mem- ory requirements. The algorithm is also furnished with a number of convergence results, including a central limit theorem.

In Paper B the problem of marginal smoothing in general hidden Markov models is tackled. A novel, PaRIS-based algorithm is presented where the marginal smoothing distributions are approximated using a lagged estimator where the lag is set adaptively.

In Paper C an estimator of the tangent filter is constructed, yield- ing in turn an estimator of the score function. The resulting algorithm is furnished with theoretical results, including a central limit theorem with a uniformly bounded variance. The resulting estimator is applied to online parameter estimation via recursive maximum liklihood.

Paper D focuses on the problem of online estimation of parameters in general hidden Markov models. The algorithm is based on a for- ward implementation of the classical expectation-maximization algo- rithm. The algorithm uses the PaRIS algorithm to achieve an efficient algorithm. 

Abstract [sv]

Denna avhandling består av fyra artiklar, presenterade i Paper A-D, som behandlar partikelbaserad online-glättning och parameter- skattning i generella dolda Markovkedjor.

I papper A presenteras en ny algoritm, PaRIS, med målet att effek- tivt beräkna partikelbaserade online-skattningar av glättade väntevär- den av additiva tillståndsfunktionaler. Algoritmen har, under svaga villkor, en beräkningskomplexitet som växer endast linjärt med antalet partiklar samt högst begränsade minneskrav. Dessutom härleds ett an- tal konvergensresultat för denna algoritm, såsom en central gränsvärdes- sats. Algoritmen testas i en simuleringsstudie.

I papper B studeras problemet att skatta marginalglättningsfördel- ningen i dolda Markovkedjor. Detta åstadkoms genom att exekvera PaRIS-algoritmen i marginalläge. Genom ett argument om mixning i Markovkedjor motiveras att avbryta uppdateringen efter en av ett stoppkriterium bestämd fördröjning vilket ger en adaptiv fördröjnings- glättare.

I papper C studeras problemet att beräkna derivator av filterfördel- ningen. Dessa används för att beräkna gradienten av log-likelihood funktionen. Algoritmen, som innehåller en uppdateringsmekanism lik- nande den i PaRIS, förses med ett antal konvergensresultat, såsom en central gränsvärdessats med en varians som är likformigt begränsad. Den resulterande algoritmen används för att konstruera en rekursiv parameterskattningsalgoritm.

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

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2017. p. 27
Series
TRITA-MAT-A ; 2017:04
National Category
Probability Theory and Statistics
Research subject
Applied and Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-215292 (URN)978-91-7729-562-4 (ISBN)
Public defence
2017-11-03, F3, Lindstedtsvägen 26, Stockholm, 09:00 (English)
Opponent
Supervisors
Note

QC 20171009

Available from: 2017-10-09 Created: 2017-10-06 Last updated: 2017-10-09Bibliographically approved

Open Access in DiVA

No full text in DiVA

Search in DiVA

By author/editor
Olsson, JimmyWesterborn, Johan
By organisation
Mathematical Statistics
Probability Theory and Statistics

Search outside of DiVA

GoogleGoogle Scholar

urn-nbn

Altmetric score

urn-nbn
Total: 5 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf