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Greedy Reduction Algorithms for Mixtures of Exponential Family
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-3450-988X
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Middle E Technical University, Turkey.
2015 (English)In: IEEE Signal Processing Letters, ISSN 1070-9908, E-ISSN 1558-2361, Vol. 22, no 6, 676-680 p.Article in journal (Refereed) Published
Abstract [en]

In this letter, we propose a general framework for greedy reduction of mixture densities of exponential family. The performances of the generalized algorithms are illustrated both on an artificial example where randomly generated mixture densities are reduced and on a target tracking scenario where the reduction is carried out in the recursion of a Gaussian inverse Wishart probability hypothesis density (PHD) filter.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE) , 2015. Vol. 22, no 6, 676-680 p.
Keyword [en]
Exponential family; extended target; integral square error; Kullback-Leibler divergence; mixture density; mixture reduction; target tracking
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
URN: urn:nbn:se:liu:diva-112990DOI: 10.1109/LSP.2014.2367154ISI: 000345236400005OAI: oai:DiVA.org:liu-112990DiVA: diva2:779192
Note

Funding Agencies|Swedish research council (VR) under ETT [621-2010-4301]; SSF, project CUAS

Available from: 2015-01-12 Created: 2015-01-08 Last updated: 2017-12-05
In thesis
1. Analytical Approximations for Bayesian Inference
Open this publication in new window or tab >>Analytical Approximations for Bayesian Inference
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Bayesian inference is a statistical inference technique in which Bayes’ theorem is used to update the probability distribution of a random variable using observations. Except for few simple cases, expression of such probability distributions using compact analytical expressions is infeasible. Approximation methods are required to express the a priori knowledge about a random variable in form of prior distributions. Further approximations are needed to compute posterior distributions of the random variables using the observations. When the computational complexity of representation of such posteriors increases over time as in mixture models, approximations are required to reduce the complexity of such representations.

This thesis further extends existing approximation methods for Bayesian inference, and generalizes the existing approximation methods in three aspects namely; prior selection, posterior evaluation given the observations and maintenance of computation complexity.

Particularly, the maximum entropy properties of the first-order stable spline kernel for identification of linear time-invariant stable and causal systems are shown. Analytical approximations are used to express the prior knowledge about the properties of the impulse response of a linear time-invariant stable and causal system.

Variational Bayes (VB) method is used to compute an approximate posterior in two inference problems. In the first problem, an approximate posterior for the state smoothing problem for linear statespace models with unknown and time-varying noise covariances is proposed. In the second problem, the VB method is used for approximate inference in state-space models with skewed measurement noise.

Moreover, a novel approximation method for Bayesian inference is proposed. The proposed Bayesian inference technique is based on Taylor series approximation of the logarithm of the likelihood function. The proposed approximation is devised for the case where the prior distribution belongs to the exponential family of distributions.

Finally, two contributions are dedicated to the mixture reduction (MR) problem. The first contribution, generalize the existing MR algorithms for Gaussian mixtures to the exponential family of distributions and compares them in an extended target tracking scenario. The second contribution, proposes a new Gaussian mixture reduction algorithm which minimizes the reverse Kullback-Leibler divergence and has specific peak preserving properties.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2015. 79 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1710
National Category
Signal Processing
Identifiers
urn:nbn:se:liu:diva-121619 (URN)10.3384/diss.diva-121619 (DOI)978-91-7685-930-8 (ISBN)
Public defence
2015-11-06, Visionen, B-huset, Campus Valla, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2015-10-05 Created: 2015-09-28 Last updated: 2015-10-07Bibliographically approved

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Ardeshiri, TohidGranström, KarlÖzkan, Emre

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