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Lindsten, Fredrik
Publications (10 of 41) Show all publications
Andersson Naesseth, C., Lindsten, F. & Schön, T. (2015). Nested Sequential Monte Carlo Methods. In: Francis Bach, David Blei (Ed.), Proceedings of The 32nd International Conference on Machine Learning: . Paper presented at 32nd International Conference on Machine Learning, Lille, France, 6-11 July, 2015 (pp. 1292-1301). Journal of Machine Learning Research (Online), 37
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: 2018-01-10Bibliographically approved
Dahlin, J., Lindsten, F. & Schön, T. (2015). Particle Metropolis-Hastings using gradient and Hessian information. Statistics and computing, 25(1), 81-92
Open this publication in new window or tab >>Particle Metropolis-Hastings using gradient and Hessian information
2015 (English)In: Statistics and computing, ISSN 0960-3174, E-ISSN 1573-1375, Vol. 25, no 1, p. 81-92Article in journal (Other academic) Published
Abstract [en]

Particle Metropolis-Hastings (PMH) allows for Bayesian parameter inference in nonlinear state space models by combining MCMC and particle filtering. The latter is used to estimate the intractable likelihood. In its original formulation, PMH makes use of a marginal MCMC proposal for the parameters, typically a Gaussian random walk. However, this can lead to a poor exploration of the parameter space and an inefficient use of the generated particles.

We propose two alternative versions of PMH that incorporate gradient and Hessian information about the posterior into the proposal. This information is more or less obtained as a byproduct of the likelihood estimation. Indeed, we show how to estimate the required information using a fixed-lag particle smoother, with a computational cost growing linearly in the number of particles. We conclude that the proposed methods can: (i) decrease the length of the burn-in phase, (ii) increase the mixing of the Markov chain at the stationary phase, and (iii) make the proposal distribution scale invariant which simplifies tuning.

Place, publisher, year, edition, pages
Springer, 2015
National Category
Control Engineering Signal Processing Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-106749 (URN)10.1007/s11222-014-9510-0 (DOI)000349028500013 ()
Projects
Probabilistic modelling of dynamical systems
Funder
Swedish Research Council, 621-2013-5524
Note

On the day of the defence date the status of this article was Manuscript.

Available from: 2014-05-21 Created: 2014-05-21 Last updated: 2017-12-05Bibliographically approved
Dahlin, J., Schön, T. B. & Lindsten, F. (2015). Quasi-Newton particle Metropolis-Hastings. In: Proceedings of the 17th IFAC Symposium on System Identification.: . Paper presented at Proceedings of the 17th IFAC Symposium on System Identification, Beijing, China, October 19-21, 2015. (pp. 981-986). Elsevier, 48 Issue 28
Open this publication in new window or tab >>Quasi-Newton particle Metropolis-Hastings
2015 (English)In: Proceedings of the 17th IFAC Symposium on System Identification., Elsevier, 2015, Vol. 48 Issue 28, p. 981-986Conference paper, Published paper (Refereed)
Abstract [en]

Particle Metropolis-Hastings enables Bayesian parameter inference in general nonlinear state space models (SSMs). However, in many implementations a random walk proposal is used and this can result in poor mixing if not tuned correctly using tedious pilot runs. Therefore, we consider a new proposal inspired by quasi-Newton algorithms that may achieve similar (or better) mixing with less tuning. An advantage compared to other Hessian based proposals, is that it only requires estimates of the gradient of the log-posterior. A possible application is parameter inference in the challenging class of SSMs with intractable likelihoods.We exemplify this application and the benefits of the new proposal by modelling log-returns offuture contracts on coffee by a stochastic volatility model with alpha-stable observations.

Place, publisher, year, edition, pages
Elsevier, 2015
Keyword
Bayesian parameter inference; state space models; approximate Bayesian computations; particle Markov chain Monte Carlo; α-stable distributions
National Category
Control Engineering Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-123666 (URN)10.1016/j.ifacol.2015.12.258 (DOI)
Conference
Proceedings of the 17th IFAC Symposium on System Identification, Beijing, China, October 19-21, 2015.
Projects
CADICS
Funder
Swedish Research Council, 637-2014-466Swedish Research Council, 621-2013-5524
Available from: 2016-01-07 Created: 2016-01-07 Last updated: 2016-04-01
Lindsten, F., Douc, R. & Moulines, E. (2015). Uniform Ergodicity of the Particle Gibbs Sampler. Scandinavian Journal of Statistics, 42(3), 775-797
Open this publication in new window or tab >>Uniform Ergodicity of the Particle Gibbs Sampler
2015 (English)In: Scandinavian Journal of Statistics, ISSN 0303-6898, E-ISSN 1467-9469, Vol. 42, no 3, p. 775-797Article in journal (Refereed) Published
Abstract [en]

The particle Gibbs sampler is a systematic way of using a particle filter within Markov chain Monte Carlo. This results in an off-the-shelf Markov kernel on the space of state trajectories, which can be used to simulate from the full joint smoothing distribution for a state space model in a Markov chain Monte Carlo scheme. We show that the particle Gibbs Markov kernel is uniformly ergodic under rather general assumptions, which we will carefully review and discuss. In particular, we provide an explicit rate of convergence, which reveals that (i) for fixed number of data points, the convergence rate can be made arbitrarily good by increasing the number of particles and (ii) under general mixing assumptions, the convergence rate can be kept constant by increasing the number of particles superlinearly with the number of observations. We illustrate the applicability of our result by studying in detail a common stochastic volatility model with a non-compact state space.

Place, publisher, year, edition, pages
Wiley, 2015
Keyword
conditional sequential Monte Carlo; particle Gibbs; particle Markov chain Monte Carlo; particle smoothing; state space models
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:liu:diva-121304 (URN)10.1111/sjos.12136 (DOI)000360077100009 ()
Note

Funding Agencies|project Learning of complex dynamical systems - Swedish Research Council [637-2014-466]

Available from: 2015-09-16 Created: 2015-09-14 Last updated: 2017-12-04
Andersson Naesseth, C., Lindsten, F. & Schön, T. (2014). Capacity estimation of two-dimensional channels using Sequential Monte Carlo. In: 2014 IEEE Information Theory Workshop: . Paper presented at Information Theory Workshop (pp. 431-435).
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: 2018-01-11
Frigola, R., Lindsten, F., Schön, T. B. & Rasmussen, C. E. (2014). Identification of Gaussian process state-space models with particle stochastic approximation EM. In: Proceedings of the 19th IFAC World Congress: . Paper presented at 19th IFAC World Congress, Cape Town, South Africa, August 24-29, 2014..
Open this publication in new window or tab >>Identification of Gaussian process state-space models with particle stochastic approximation EM
2014 (English)In: Proceedings of the 19th IFAC World Congress, 2014Conference paper, Published paper (Refereed)
Abstract [en]

Gaussian process state-space models (GP-SSMs) are a very exible family of models of nonlinear dynamical systems. They comprise a Bayesian nonparametric representation of the dynamics of the system and additional (hyper-)parameters governing the properties of this nonparametric representation. The Bayesian formalism enables systematic reasoning about the uncertainty in the system dynamics. We present an approach to maximum likelihood identification of the parameters in GP-SSMs, while retaining the full nonparametric description of the dynamics. The method is based on a stochastic approximation version of the EM algorithm that employs recent developments in particle Markov chain Monte Carlo for efficient identification.

National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-110058 (URN)
Conference
19th IFAC World Congress, Cape Town, South Africa, August 24-29, 2014.
Projects
CADICS
Available from: 2014-09-02 Created: 2014-09-02 Last updated: 2014-12-17
Dahlin, J. & Lindsten, F. (2014). Particle filter-based Gaussian process optimisation for parameter inference. In: Edward Boje and Xiaohua Xia (Ed.), Proceedings of the 19th IFAC World Congress, 2014: . Paper presented at 19th IFAC World Congress, Cape Town, South Africa, August 24-29 (pp. 8675-8680).
Open this publication in new window or tab >>Particle filter-based Gaussian process optimisation for parameter inference
2014 (English)In: Proceedings of the 19th IFAC World Congress, 2014 / [ed] Edward Boje and Xiaohua Xia, 2014, p. 8675-8680Conference paper, Published paper (Refereed)
Abstract [en]

We propose a novel method for maximum-likelihood-based parameter inference in nonlinear and/or non-Gaussian state space models. The method is an iterative procedure with three steps. At each iteration a particle filter is used to estimate the value of the log-likelihood function at the current parameter iterate. Using these log-likelihood estimates, a surrogate objective function is created by utilizing a Gaussian process model. Finally, we use a heuristic procedure to obtain a revised parameter iterate, providing an automatic trade-off between exploration and exploitation of the surrogate model. The method is profiled on two state space models with good performance both considering accuracy and computational cost.

Series
World Congress,, ISSN 1474-6670 ; Volume 19, Part 1
Keyword
Particle filtering/Monte Carlo methods; Bayesian methods; Nonlinear system identification
National Category
Control Engineering Signal Processing Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-106750 (URN)10.3182/20140824-6-ZA-1003.00278 (DOI)978-3-902823-62-5 (ISBN)
Conference
19th IFAC World Congress, Cape Town, South Africa, August 24-29
Projects
Probabilistic modelling of dynamical systems
Funder
Swedish Research Council, 621-2013-5524
Available from: 2014-05-21 Created: 2014-05-21 Last updated: 2016-05-04Bibliographically approved
Gunnarsson, F., Lindsten, F. & Carlsson, N. (2014). Particle filtering for network-based positioning terrestrial radio networks. In: Data Fusion & Target Tracking 2014: Algorithms and Applications (DF&TT 2014), IET Conference on: . Paper presented at IET Conference on Data Fusion and Target Tracking 2014: Algorithms and Applications. Institution of Engineering and Technology, 2014(629 CP)
Open this publication in new window or tab >>Particle filtering for network-based positioning terrestrial radio networks
2014 (English)In: Data Fusion & Target Tracking 2014: Algorithms and Applications (DF&TT 2014), IET Conference on, Institution of Engineering and Technology , 2014, Vol. 2014, no 629 CPConference paper, Published paper (Refereed)
Abstract [en]

There is strong interest in positioing in wireless networks, partly to support end user service needs, but also to support network management with network-based network information. The focus in this paper is on the latter, while using measurements that are readily available in wireless networks. We show how thesignal direction of departure and inter-distance between the base station and the mobile terminal can be estimated, and how particle filters and smoothers can be used to post-process the measurements. The methods are evaluated in a live 3GPP LTE network with promising results inlcuding position error medians of less than 100 m.

Place, publisher, year, edition, pages
Institution of Engineering and Technology, 2014
Series
IET Conference Publications Series
National Category
Communication Systems
Identifiers
urn:nbn:se:liu:diva-116743 (URN)10.1049/cp.2014.0523 (DOI)2-s2.0-84902687636 (Scopus ID)9781849198639 (ISBN)
Conference
IET Conference on Data Fusion and Target Tracking 2014: Algorithms and Applications
Note

Funding Agencies|SSF, Swedish Foundation for Strategic Research

Available from: 2015-04-09 Created: 2015-04-02 Last updated: 2015-04-20
Lindsten, F., Jordan, M. I. & Schon, T. B. (2014). Particle Gibbs with Ancestor Sampling. Journal of machine learning research, 15, 2145-2184
Open this publication in new window or tab >>Particle Gibbs with Ancestor Sampling
2014 (English)In: Journal of machine learning research, ISSN 1532-4435, E-ISSN 1533-7928, Vol. 15, p. 2145-2184Article in journal (Refereed) Published
Abstract [en]

Particle Markov chain Monte Carlo (PMCMC) is a systematic way of combining the two main tools used for Monte Carlo statistical inference: sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC). We present a new PMCMC algorithm that we refer to as particle Gibbs with ancestor sampling (PGAS). PGAS provides the data analyst with an off-the-shelf class of Markov kernels that can be used to simulate, for instance, the typically high-dimensional and highly autocorrelated state trajectory in a state-space model. The ancestor sampling procedure enables fast mixing of the PGAS kernel even when using seemingly few particles in the underlying SMC sampler. This is important as it can significantly reduce the computational burden that is typically associated with using SMC. PGAS is conceptually similar to the existing PG with backward simulation (PGBS) procedure. Instead of using separate forward and backward sweeps as in PGBS, however, we achieve the same effect in a single forward sweep. This makes PGAS well suited for addressing inference problems not only in state-space models, but also in models with more complex dependencies, such as non-Markovian, Bayesian nonparametric, and general probabilistic graphical models.

Place, publisher, year, edition, pages
MICROTOME PUBL, 2014
Keyword
particle Markov chain Monte Carlo; sequential Monte Carlo; Bayesian inference; non-Markovian models; state-space models
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:liu:diva-112843 (URN)000344638300009 ()
Note

Funding Agencies|project Probabilistic modelling of dynamical systems - Swedish Research Council [621-2013-5524]; CADICS; Linnaeus Center - Swedish Research Council; project Bayesian Tracking and Reasoning over Time - EPSRC [EP/K020153/1]

Available from: 2015-01-08 Created: 2014-12-17 Last updated: 2017-12-05
Dahlin, J., Lindsten, F. & Schön, T. (2014). Second-Order Particle MCMC for Bayesian Parameter Inference. In: Proceedings of the 19th IFAC World Congress: . Paper presented at 19th IFAC World Congress, Cape Town, South Africa, August 24-29, 2014 (pp. 8656-8661).
Open this publication in new window or tab >>Second-Order Particle MCMC for Bayesian Parameter Inference
2014 (English)In: Proceedings of the 19th IFAC World Congress, 2014, p. 8656-8661Conference paper, Published paper (Refereed)
Abstract [en]

We propose an improved proposal distribution in the Particle Metropolis-Hastings (PMH) algorithm for Bayesian parameter inference in nonlinear state space models. This proposal incorporates second-order information about the parameter posterior distribution, which can be extracted from the particle filter already used within the PMH algorithm. The added information makes the proposal scale-invariant, simpler to tune and can possibly also shorten the burn-in phase. The proposed algorithm has a computational cost which is proportional to the number of particles, i.e. the same as the original marginal PMH algorithm. Finally, we provide two numerical examples that illustrates some of the possible benefits of adding the second-order information.

Keyword
Particle filtering/Monte Carlo methods; Nonlinear system identification; Bayesian methods
National Category
Control Engineering Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-113997 (URN)10.3182/20140824-6-ZA-1003.00277 (DOI)
Conference
19th IFAC World Congress, Cape Town, South Africa, August 24-29, 2014
Projects
CADICS
Funder
Swedish Research Council, 621-2013-5524
Available from: 2015-02-05 Created: 2015-02-05 Last updated: 2016-05-04
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