| 1. |
- Özkan, Emre, et al.
(författare)
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Recursive Maximum Likelihood Identification of Jump Markov Nonlinear Systems
- 2015
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Ingår i: IEEE Transactions on Signal Processing. - : Institute of Electrical and Electronics Engineers (IEEE). - 1053-587X .- 1941-0476. ; 63:3, s. 754-765
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Tidskriftsartikel (refereegranskat)abstract
- We present an online method for joint state and parameter estimation in jump Markov non-linear systems (JMNLS). State inference is enabled via the use of particle filters which makes the method applicable to a wide range of non-linear models. To exploit the inherent structure of JMNLS, we design a Rao-Blackwellized particle filter (RBPF) where the discrete mode is marginalized out analytically. This results in an efficient implementation of the algorithm and reduces the estimation error variance. The proposed RBPF is then used to compute, recursively in time, smoothed estimates of complete data sufficient statistics. Together with the online expectation maximization algorithm, this enables recursive identification of unknown model parameters including the transition probability matrix. The method is also applicable to online identification of jump Markov linear systems(JMLS). The performance of the method is illustrated in simulations and on a localization problem in wireless networks using real data.
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| 2. |
- Andersson Naesseth, Christian, 1986-
(författare)
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Machine learning using approximate inference : Variational and sequential Monte Carlo methods
- 2018
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Automatic decision making and pattern recognition under uncertainty are difficult tasks that are ubiquitous in our everyday life. The systems we design, and technology we develop, requires us to coherently represent and work with uncertainty in data. Probabilistic models and probabilistic inference gives us a powerful framework for solving this problem. Using this framework, while enticing, results in difficult-to-compute integrals and probabilities when conditioning on the observed data. This means we have a need for approximate inference, methods that solves the problem approximately using a systematic approach. In this thesis we develop new methods for efficient approximate inference in probabilistic models.There are generally two approaches to approximate inference, variational methods and Monte Carlo methods. In Monte Carlo methods we use a large number of random samples to approximate the integral of interest. With variational methods, on the other hand, we turn the integration problem into that of an optimization problem. We develop algorithms of both types and bridge the gap between them.First, we present a self-contained tutorial to the popular sequential Monte Carlo (SMC) class of methods. Next, we propose new algorithms and applications based on SMC for approximate inference in probabilistic graphical models. We derive nested sequential Monte Carlo, a new algorithm particularly well suited for inference in a large class of high-dimensional probabilistic models. Then, inspired by similar ideas we derive interacting particle Markov chain Monte Carlo to make use of parallelization to speed up approximate inference for universal probabilistic programming languages. After that, we show how we can make use of the rejection sampling process when generating gamma distributed random variables to speed up variational inference. Finally, we bridge the gap between SMC and variational methods by developing variational sequential Monte Carlo, a new flexible family of variational approximations.
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| 3. |
- Lindsten, Fredrik, 1984-, et al.
(författare)
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Divide-and-Conquer With Sequential Monte Carlo
- 2017
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Ingår i: Journal of Computational And Graphical Statistics. - : AMER STATISTICAL ASSOC. - 1061-8600 .- 1537-2715. ; 26:2, s. 445-458
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Tidskriftsartikel (refereegranskat)abstract
- We propose a novel class of Sequential Monte Carlo (SMC) algorithms, appropriate for inference in probabilistic graphical models. This class of algorithms adopts a divide-and-conquer approach based upon an auxiliary tree-structured decomposition of the model of interest, turning the overall inferential task into a collection of recursively solved subproblems. The proposed method is applicable to a broad class of probabilistic graphical models, including models with loops. Unlike a standard SMC sampler, the proposed divide-and-conquer SMC employs multiple independent populations of weighted particles, which are resampled, merged, and propagated as the method progresses. We illustrate empirically that this approach can outperform standard methods in terms of the accuracy of the posterior expectation and marginal likelihood approximations. Divide-and-conquer SMC also opens up novel parallel implementation options and the possibility of concentrating the computational effort on the most challenging subproblems. We demonstrate its performance on a Markov random field and on a hierarchical logistic regression problem. Supplementary materials including proofs and additional numerical results are available online.
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| 4. |
- Naesseth, Christian A., et al.
(författare)
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Elements of Sequential Monte Carlo
- 2019
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Ingår i: FOUNDATIONS AND TRENDS IN MACHINE LEARNING. - : NOW PUBLISHERS INC. - 1935-8237 .- 1935-8245. ; 12:3, s. 187-306
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Tidskriftsartikel (refereegranskat)abstract
- A core problem in statistics and probabilistic machine learning is to compute probability distributions and expectations. This is the fundamental problem of Bayesian statistics and machine learning, which frames all inference as expectations with respect to the posterior distribution. The key challenge is to approximate these intractable expectations. In this tutorial, we review sequential Monte Carlo (SMC), a random-sampling-based class of methods for approximate inference. First, we explain the basics of SMC, discuss practical issues, and review theoretical results. We then examine two of the main user design choices: the proposal distributions and the so called intermediate target distributions. We review recent results on how variational inference and amortization can be used to learn efficient proposals and target distributions. Next, we discuss the SMC estimate of the normalizing constant, how this can be used for pseudo-marginal inference and inference evaluation. Throughout the tutorial we illustrate the use of SMC on various models commonly used in machine learning, such as stochastic recurrent neural networks, probabilistic graphical models, and probabilistic programs.
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| 5. |
- Rainforth, Tom, et al.
(författare)
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Interacting Particle Markov Chain Monte Carlo
- 2016
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Ingår i: Proceedings of the 33rd International Conference on Machine Learning (ICML). ; , s. 2616-2625
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Konferensbidrag (refereegranskat)abstract
- We introduce interacting particle Markov chain Monte Carlo (iPMCMC), a PMCMC method based on an interacting pool of standard and conditional sequential Monte Carlo samplers. Like related methods, iPMCMC is a Markov chain Monte Carlo sampler on an extended space. We present empirical results that show significant improvements in mixing rates relative to both non-interacting PMCMC samplers and a single PMCMC sampler with an equivalent memory and computational budget. An additional advantage of the iPMCMC method is that it is suitable for distributed and multi-core architectures.
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| 6. |
- Riabiz, Marina, et al.
(författare)
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Pseudo-Marginal MCMC for Parameter Estimation in Alpha-Stable Distributions
- 2015
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Ingår i: Proceedings of the 17th IFAC Symposium on System Identification (SYSID). - : Elsevier. ; , s. 472-477
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Konferensbidrag (refereegranskat)abstract
- The α-stable distribution is very useful for modelling data with extreme values and skewed behaviour. The distribution is governed by two key parameters, tail thickness and skewness, in addition to scale and location. Inferring these parameters is difficult due to the lack of a closed form expression of the probability density. We develop a Bayesian method, based on the pseudo-marginal MCMC approach, that requires only unbiased estimates of the intractable likelihood. To compute these estimates we build an adaptive importance sampler for a latentvariable- representation of the α-stable density. This representation has previously been used in the literature for conditional MCMC sampling of the parameters, and we compare our method with this approach.
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| 7. |
- 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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| 8. |
- Vaicenavicius, Juozas, et al.
(författare)
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Evaluating model calibration in classification
- 2019
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Ingår i: Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics.
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Konferensbidrag (refereegranskat)abstract
- Probabilistic classifiers output a probability distribution on target classes rather than just a class prediction. Besides providing a clear separation of prediction and decision making, the main advantage of probabilistic models is their ability to represent uncertainty about predictions. In safetycritical applications, it is pivotal for a model to possess an adequate sense of uncertainty, which for probabilistic classifiers translates into outputting probability distributions that are consistent with the empirical frequencies observed from realized outcomes. A classifier with such a property is called calibrated. In this work, we develop a general theoretical calibration evaluation framework grounded in probability theory, and point out subtleties present in model calibration evaluation that lead to refined interpretations of existing evaluation techniques. Lastly, we propose new ways to quantify and visualize miscalibration in probabilistic classification, including novel multidimensional reliability diagrams.
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| 9. |
- Wågberg, Johan, et al.
(författare)
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Bayesian nonparametric identification of piecewise affine ARX systems
- 2015
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Ingår i: 17th IFAC Symposium on System IdentificationSYSID 2015 Proceedings. - : Elsevier. ; , s. 709-714
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Konferensbidrag (refereegranskat)abstract
- We introduce a Bayesian nonparametric approach to identification of piecewise affine ARX systems. The clustering properties of the Dirichlet process are used to construct a prior over the partition of the regressor space as well as the parameters of each local model. This enables us to probabilistically reason about and to identify the number of modes, the partition of the regressor space, and the linear dynamics of each local model from data. By appropriate choices of base measure and likelihood function, we give explicit expressions for how to perform both inference and prediction. Simulations and experiments on real data from a pick and place machine are used to illustrate the capabilities of the new approach.
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| 10. |
- Wågberg, Johan, et al.
(författare)
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Bayesian nonparametric identification of piecewise affine ARX systems
- 2015
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Ingår i: IFAC-PapersOnLine. - : Elsevier BV. - 2405-8963. ; , s. 709-714
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Konferensbidrag (refereegranskat)abstract
- We introduce a Bayesian nonparametric approach to identification of piecewise affine ARX systems. The clustering properties of the Dirichlet process are used to construct a prior over the partition of the regressor space as well as the parameters of each local model. This enables us to probabilistically reason about and to identify the number of modes, the partition of the regressor space, and the linear dynamics of each local model from data. By appropriate choices of base measure and likelihood function, we give explicit expressions for how to perform both inference and prediction. Simulations and experiments on real data from a pick and place machine are used to illustrate the capabilities of the new approach.
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