| 1. |
- Schön, Thomas Bo, et al.
(författare)
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Sequential Monte Carlo Methods for System Identification
- 2015
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Ingår i: Proceedings of the 17th IFAC Symposium on System Identification.. - : Elsevier. ; , s. 775-786
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Konferensbidrag (refereegranskat)abstract
- One of the key challenges in identifying nonlinear and possibly non-Gaussian state space models (SSMs) is the intractability of estimating the system state. Sequential Monte Carlo (SMC) methods, such as the particle filter (introduced more than two decades ago), provide numerical solutions to the nonlinear state estimation problems arising in SSMs. When combined with additional identification techniques, these algorithms provide solid solutions to the nonlinear system identification problem. We describe two general strategies for creating such combinations and discuss why SMC is a natural tool for implementing these strategies.
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| 2. |
- Alenlöv, Johan, et al.
(författare)
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Pseudo-Marginal Hamiltonian Monte Carlo
- 2021
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Ingår i: Journal of machine learning research. - : MICROTOME PUBL. - 1532-4435 .- 1533-7928. ; 22
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Tidskriftsartikel (refereegranskat)abstract
- Bayesian inference in the presence of an intractable likelihood function is computationally challenging. When following a Markov chain Monte Carlo (MCMC) approach to approximate the posterior distribution in this context, one typically either uses MCMC schemes which target the joint posterior of the parameters and some auxiliary latent variables, or pseudo-marginal Metropolis-Hastings (MH) schemes. The latter mimic a MH algorithm targeting the marginal posterior of the parameters by approximating unbiasedly the intractable likelihood. However, in scenarios where the parameters and auxiliary variables are strongly correlated under the posterior and/or this posterior is multimodal, Gibbs sampling or Hamiltonian Monte Carlo (HMC) will perform poorly and the pseudo-marginal MH algorithm, as any other MH scheme, will be inefficient for high-dimensional parameters. We propose here an original MCMC algorithm, termed pseudo-marginal HMC, which combines the advantages of both HMC and pseudo-marginal schemes. Specifically, the PM-HMC method is controlled by a precision parameter N, controlling the approximation of the likelihood and, for any N, it samples the marginal posterior of the parameters. Additionally, as N tends to infinity, its sample trajectories and acceptance probability converge to those of an ideal, but intractable, HMC algorithm which would have access to the intractable likelihood and its gradient. We demonstrate through experiments that PM-HMC can outperform significantly both standard HMC and pseudo-marginal MH schemes.
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| 3. |
- Dahlin, Johan, 1986-
(författare)
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Accelerating Monte Carlo methods for Bayesian inference in dynamical models
- 2016
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Making decisions and predictions from noisy observations are two important and challenging problems in many areas of society. Some examples of applications are recommendation systems for online shopping and streaming services, connecting genes with certain diseases and modelling climate change. In this thesis, we make use of Bayesian statistics to construct probabilistic models given prior information and historical data, which can be used for decision support and predictions. The main obstacle with this approach is that it often results in mathematical problems lacking analytical solutions. To cope with this, we make use of statistical simulation algorithms known as Monte Carlo methods to approximate the intractable solution. These methods enjoy well-understood statistical properties but are often computational prohibitive to employ.The main contribution of this thesis is the exploration of different strategies for accelerating inference methods based on sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC). That is, strategies for reducing the computational effort while keeping or improving the accuracy. A major part of the thesis is devoted to proposing such strategies for the MCMC method known as the particle Metropolis-Hastings (PMH) algorithm. We investigate two strategies: (i) introducing estimates of the gradient and Hessian of the target to better tailor the algorithm to the problem and (ii) introducing a positive correlation between the point-wise estimates of the target.Furthermore, we propose an algorithm based on the combination of SMC and Gaussian process optimisation, which can provide reasonable estimates of the posterior but with a significant decrease in computational effort compared with PMH. Moreover, we explore the use of sparseness priors for approximate inference in over-parametrised mixed effects models and autoregressive processes. This can potentially be a practical strategy for inference in the big data era. Finally, we propose a general method for increasing the accuracy of the parameter estimates in non-linear state space models by applying a designed input signal.
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| 4. |
- Dahlin, Johan, 1986-, et al.
(författare)
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Hierarchical Bayesian approaches for robust inference in ARX models
- 2012
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Ingår i: Proceedings from the 16th IFAC Symposium on System Identification, 2012. - : International Federation of Automatic Control. - 9783902823069 ; , s. 131-136
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Konferensbidrag (refereegranskat)abstract
- Gaussian innovations are the typical choice in most ARX models but using other distributions such as the Student's t could be useful. We demonstrate that this choice of distribution for the innovations provides an increased robustness to data anomalies, such as outliers and missing observations. We consider these models in a Bayesian setting and perform inference using numerical procedures based on Markov Chain Monte Carlo methods. These models include automatic order determination by two alternative methods, based on a parametric model order and a sparseness prior, respectively. The methods and the advantage of our choice of innovations are illustrated in three numerical studies using both simulated data and real EEG data.
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| 5. |
- Dahlin, Johan, 1986-, et al.
(författare)
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Particle filter-based Gaussian process optimisation for parameter inference
- 2014
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Ingår i: Proceedings of the 19th IFAC World Congress, 2014. - 9783902823625 ; , s. 8675-8680
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Konferensbidrag (refereegranskat)abstract
- 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.
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| 6. |
- Dahlin, Johan, 1986-, et al.
(författare)
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Particle Metropolis-Hastings using gradient and Hessian information
- 2015
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Ingår i: Statistics and computing. - : Springer. - 0960-3174 .- 1573-1375. ; 25:1, s. 81-92
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 7. |
- Dahlin, Johan, 1986-, et al.
(författare)
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Particle Metropolis Hastings using Langevin Dynamics
- 2013
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Ingår i: Proceedings of the 38th International Conference on Acoustics, Speech, and Signal Processing. - : IEEE conference proceedings. ; , s. 6308-6312
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Konferensbidrag (refereegranskat)abstract
- Particle Markov Chain Monte Carlo (PMCMC) samplers allow for routine inference of parameters and states in challenging nonlinear problems. A common choice for the parameter proposal is a simple random walk sampler, which can scale poorly with the number of parameters.In this paper, we propose to use log-likelihood gradients, i.e. the score, in the construction of the proposal, akin to the Langevin Monte Carlo method, but adapted to the PMCMC framework. This can be thought of as a way to guide a random walk proposal by using drift terms that are proportional to the score function. The method is successfully applied to a stochastic volatility model and the drift term exhibits intuitive behaviour.
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| 8. |
- Dahlin, Johan, 1986-, et al.
(författare)
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Quasi-Newton particle Metropolis-Hastings
- 2015
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Ingår i: Proceedings of the 17th IFAC Symposium on System Identification.. - : Elsevier. ; , s. 981-986
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Konferensbidrag (refereegranskat)abstract
- 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.
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| 9. |
- Dahlin, Johan, 1986-, et al.
(författare)
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Robust ARX Models with Automatic Order Determination and Student's t Innovations
- 2011
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- ARX models is a common class of models of dynamical systems. Here, we consider the case when the innovation process is not well described by Gaussian noise and instead propose to model the driving noise as Student's t distributed. The t distribution is more heavy tailed than the Gaussian distribution, which provides an increased robustness to data anomalies, such as outliers and missing observations. We use a Bayesian setting and design the models to also include an automatic order determination. Basically, this means that we infer knowledge about the posterior distribution of the model order from data. We consider two related models, one with a parametric model order and one with a sparseness prior on the ARX coefficients. We derive Markov chain Monte Carlo samplers to perform inference in these models. Finally, we provide three numerical illustrations with both simulated data and real EEG data to evaluate the proposed methods.
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| 10. |
- Dahlin, Johan, 1986-, et al.
(författare)
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Second-Order Particle MCMC for Bayesian Parameter Inference
- 2014
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Ingår i: Proceedings of the 19th IFAC World Congress. ; , s. 8656-8661
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Konferensbidrag (refereegranskat)abstract
- 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.
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