liu.seSearch for publications in DiVA
Change search
Link to record
Permanent link

Direct link
BETA
Schön, Thomas
Alternative names
Publications (10 of 159) Show all publications
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
Valenzuela, P. E., Dahlin, J., Rojas, C. R. & Schön, T. (2014). A graph/particle-based method for experiment design in nonlinear systems. 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. 1404-1409). International Federation of Automatic Control
Open this publication in new window or tab >>A graph/particle-based method for experiment design in nonlinear systems
2014 (English)In: Proceedings of the 19th IFAC World Congress, 2014 / [ed] Edward Boje and Xiaohua Xia, International Federation of Automatic Control , 2014, p. 1404-1409Conference paper, Published paper (Refereed)
Abstract [en]

We propose an extended method for experiment design in nonlinear state space models. The proposed input design technique optimizes a scalar cost function of the information matrix, by computing the optimal stationary probability mass function (pmf) from which an input sequence is sampled. The feasible set of the stationary pmf is a polytope, allowing it to be expressed as a convex combination of its extreme points. The extreme points in the feasible set of pmf’s can be computed using graph theory. Therefore, the final information matrix can be approximated as a convex combination of the information matrices associated with each extreme point. For nonlinear systems, the information matrices for each extreme point can be computed by using particle methods. Numerical examples show that the proposed techniquecan be successfully employed for experiment design in nonlinear systems.

Place, publisher, year, edition, pages
International Federation of Automatic Control, 2014
Series
World Congress, ISSN 1474-6670 ; Volumen 19, Part 1
National Category
Control Engineering Signal Processing Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-106751 (URN)10.3182/20140824-6-ZA-1003.00361 (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
Dahlin, J., Schön, T. B. & Villani, M. (2014). Approximate inference in state space models with intractable likelihoods using Gaussian process optimisation.
Open this publication in new window or tab >>Approximate inference in state space models with intractable likelihoods using Gaussian process optimisation
2014 (English)Report (Other academic)
Abstract [en]

We propose a novel method for MAP parameter inference in nonlinear state space models with intractable likelihoods. The method is based on a combination of Gaussian process optimisation (GPO), sequential Monte Carlo (SMC) and approximate Bayesian computations (ABC). SMC and ABC are used to approximate the intractable likelihood by using the similarity between simulated realisations from the model and the data obtained from the system. The GPO algorithm is used for the MAP parameter estimation given noisy estimates of the log-likelihood. The proposed parameter inference method is evaluated in three problems using both synthetic and real-world data. The results are promising, indicating that the proposed algorithm converges fast and with reasonable accuracy compared with existing methods.

Publisher
p. 25
Series
LiTH-ISY-R, ISSN 1400-3902 ; 3075
Keyword
Approximate Bayesian computations, Gaussian process optimisation, Bayesian parameter inference, alpha-stable distribution
National Category
Probability Theory and Statistics Control Engineering Signal Processing
Identifiers
urn:nbn:se:liu:diva-106198 (URN)LiTH-ISY-R-3075 (ISRN)
Funder
Swedish Research Council, 621-2013-5524
Available from: 2014-04-28 Created: 2014-04-28 Last updated: 2016-05-04Bibliographically approved
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
Kronander, J., Dahlin, J., Jönsson, D., Kok, M., Schön, T. & Unger, J. (2014). Real-time video based lighting using GPU raytracing. In: Proceedings of the 22nd European Signal Processing Conference (EUSIPCO), 2014: . Paper presented at 22nd European Signal Processing Conference (EUSIPCO 2014), 1-5 September 2014, Lisbon, Portugal. IEEE Signal Processing Society
Open this publication in new window or tab >>Real-time video based lighting using GPU raytracing
Show others...
2014 (English)In: Proceedings of the 22nd European Signal Processing Conference (EUSIPCO), 2014, IEEE Signal Processing Society, 2014Conference paper, Published paper (Refereed)
Abstract [en]

The recent introduction of HDR video cameras has enabled the development of image based lighting techniques for rendering virtual objects illuminated with temporally varying real world illumination. A key challenge in this context is that rendering realistic objects illuminated with video environment maps is computationally demanding. In this work, we present a GPU based rendering system based on the NVIDIA OptiX framework, enabling real time raytracing of scenes illuminated with video environment maps. For this purpose, we explore and compare several Monte Carlo sampling approaches, including bidirectional importance sampling, multiple importance sampling and sequential Monte Carlo samplers. While previous work have focused on synthetic data and overly simple environment maps sequences, we have collected a set of real world dynamic environment map sequences using a state-of-art HDR video camera for evaluation and comparisons.

Place, publisher, year, edition, pages
IEEE Signal Processing Society, 2014
Keyword
High dynamic range imaging, image synthesis, iamge based lighting
National Category
Signal Processing
Identifiers
urn:nbn:se:liu:diva-107638 (URN)
Conference
22nd European Signal Processing Conference (EUSIPCO 2014), 1-5 September 2014, Lisbon, Portugal
Projects
VPS
Funder
Swedish Foundation for Strategic Research , IISS-0081
Available from: 2014-06-17 Created: 2014-06-17 Last updated: 2016-05-04Bibliographically approved
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
Andersson Naesseth, C., Lindsten, F. & Schön, T. (2014). Sequential Monte Carlo for Graphical Models. In: Advances in Neural Information Processing Systems: . Paper presented at Neural Information Processing Systems (NIPS) (pp. 1862-1870).
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: 2018-01-11Bibliographically approved
Taghavi, E., Lindsten, F., Svensson, L. & Schön, T. B. (2013). Adaptive stopping for fast particle smoothing. In: Proceedings of the 38th International Conference on Acoustics, Speech, and Signal Processing (ICASSP): . Paper presented at 38th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013; Vancouver, BC; Canada (pp. 6293-6297). IEEE
Open this publication in new window or tab >>Adaptive stopping for fast particle smoothing
2013 (English)In: Proceedings of the 38th International Conference on Acoustics, Speech, and Signal Processing (ICASSP), IEEE , 2013, p. 6293-6297Conference paper, Published paper (Refereed)
Abstract [en]

Particle smoothing is useful for offline state inference and parameter learning in nonlinear/non-Gaussian state-space models. However, many particle smoothers, such as the popular forward filter/backward simulator (FFBS), are plagued by a quadratic computational complexity in the number of particles. One approach to tackle this issue is to use rejection-sampling-based FFBS (RS-FFBS), which asymptotically reaches linear complexity. In practice, however, the constants can be quite large and the actual gain in computational time limited. In this contribution, we develop a hybrid method, governed by an adaptive stopping rule, in order to exploit the benefits, but avoid the drawbacks, of RS-FFBS. The resulting particle smoother is shown in a simulation study to be considerably more computationally efficient than both FFBS and RS-FFBS.

Place, publisher, year, edition, pages
IEEE, 2013
Keyword
Sequential Monte Carlo, particle smoothing, backward simulation
National Category
Signal Processing Control Engineering
Identifiers
urn:nbn:se:liu:diva-93461 (URN)10.1109/ICASSP.2013.6638876 (DOI)978-147990356-6 (ISBN)
Conference
38th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013; Vancouver, BC; Canada
Projects
CNDMCADICS
Funder
Swedish Research Council, 621-2010-5876
Available from: 2013-06-03 Created: 2013-06-03 Last updated: 2014-12-02
Lindsten, F. & Schön, T. B. (2013). Backward simulation methods for Monte Carlo statistical inference. Foundations and Trends in Machine Learning, 6(1), 1-143
Open this publication in new window or tab >>Backward simulation methods for Monte Carlo statistical inference
2013 (English)In: Foundations and Trends in Machine Learning, ISSN 1935-8237, Vol. 6, no 1, p. 1-143Article in journal (Refereed) Published
Abstract [en]

Monte Carlo methods, in particular those based on Markov chains and on interacting particle systems, are by now tools that are routinely used in machine learning. These methods have had a profound impact on statistical inference in a wide range of application areas where probabilistic models are used. Moreover, there are many algorithms in machine learning which are based on the idea of processing the data sequentially, first in the forward direction and then in the backward direction. In this tutorial we will review a branch of Monte Carlo methods based on the forward-backward idea, referred to as backward simulators. These methods are useful for learning and inference in probabilistic models containing latent stochastic processes. The theory and practice of backward simulation algorithms have undergone a significant development in recent years and the algorithms keep finding new applications. The foundation for these methods is sequential Monte Carlo (SMC). SMC-based backward simulators are capable of addressing smoothing problems in sequential latent variable models, such as general, nonlinear/non-Gaussian state-space models (SSMs). However, we will also clearly show that the underlying backward simulation idea is by no means restricted to SSMs. Furthermore, backward simulation plays an important role in recent developments of Markov chain Monte Carlo (MCMC) methods. Particle MCMC is a systematic way of using SMC within MCMC. In this framework, backward simulation gives us a way to significantly improve the performance of the samplers. We review and discuss several related backward-simulation-based methods for state inference as well as learning of static parameters, both using a frequentistic and a Bayesian approach.

Keyword
Bayesian learning, Markov chain Monte Carlo, Nonlinear signal processing, Particle smoothing, Sequential Monte Carlo
National Category
Control Engineering Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-98294 (URN)10.1561/2200000045 (DOI)
Projects
CNDMCADICS
Funder
Swedish Research Council
Available from: 2013-10-07 Created: 2013-10-07 Last updated: 2013-10-08
Lindsten, F., Schön, T. & Jordan, M. I. (2013). Bayesian semiparametric Wiener system identification. Automatica, 49(7), 2053-2063
Open this publication in new window or tab >>Bayesian semiparametric Wiener system identification
2013 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 49, no 7, p. 2053-2063Article in journal (Refereed) Published
Abstract [en]

We present a novel method for Wiener system identification. The method relies on a semiparametric, i.e. a mixed parametric/nonparametric, model of a Wiener system. We use a state-space model for the linear dynamical system and a nonparametric Gaussian process model for the static nonlinearity. We avoid making strong assumptions, such as monotonicity, on the nonlinear mapping. Stochastic disturbances, entering both as measurement noise and as process noise, are handled in a systematic manner. The nonparametric nature of the Gaussian process allows us to handle a wide range of nonlinearities without making problem-specific parameterizations. We also consider sparsity-promoting priors, based on generalized hyperbolic distributions, to automatically infer the order of the underlying dynamical system. We derive an inference algorithm based on an efficient particle Markov chain Monte Carlo method, referred to as particle Gibbs with ancestor sampling. The method is profiled on two challenging identification problems with good results. Blind Wiener system identification is handled as a special case.

Place, publisher, year, edition, pages
Elsevier, 2013
Keyword
System identification, Wiener, Block-oriented models, Gaussian process, Semiparametric, Particle filter, Ancestor sampling, Particle Markov chain Monte Carlo
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-95954 (URN)10.1016/j.automatica.2013.03.021 (DOI)000321233900011 ()
Note

Funding Agencies|project Calibrating Nonlinear Dynamical Models|621-2010-5876|Swedish Research Council||CADICS||Linnaeus Center||

Available from: 2013-08-19 Created: 2013-08-12 Last updated: 2017-12-06
Organisations

Search in DiVA

Show all publications