| 1. |
- Murray, Lawrence, et al.
(författare)
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Delayed sampling and automatic Rao-Blackwellization of probabilistic programs
- 2018
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Ingår i: Proceedings of the 21st International Conference on Artificial Intelligence and Statistics (AISTATS), Lanzarote, Spain, April, 2018. - : PMLR.
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Konferensbidrag (refereegranskat)abstract
- We introduce a dynamic mechanism for the solution of analytically-tractable substructure in probabilistic programs, using conjugate priors and affine transformations to reduce variance in Monte Carlo estimators. For inference with Sequential Monte Carlo, this automatically yields improvements such as locallyoptimal proposals and Rao–Blackwellization. The mechanism maintains a directed graph alongside the running program that evolves dynamically as operations are triggered upon it. Nodes of the graph represent random variables, edges the analytically-tractable relationships between them. Random variables remain in the graph for as long as possible, to be sampled only when they are used by the program in a way that cannot be resolved analytically. In the meantime, they are conditioned on as many observations as possible. We demonstrate the mechanism with a few pedagogical examples, as well as a linearnonlinear state-space model with simulated data, and an epidemiological model with real data of a dengue outbreak in Micronesia. In all cases one or more variables are automatically marginalized out to significantly reduce variance in estimates of the marginal likelihood, in the final case facilitating a randomweight or pseudo-marginal-type importance sampler for parameter estimation. We have implemented the approach in Anglican and a new probabilistic programming language called Birch.
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| 2. |
- Andersson, Carl
(författare)
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Deep learning applied to system identification : A probabilistic approach
- 2019
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Machine learning has been applied to sequential data for a long time in the field of system identification. As deep learning grew under the late 00's machine learning was again applied to sequential data but from a new angle, not utilizing much of the knowledge from system identification. Likewise, the field of system identification has yet to adopt many of the recent advancements in deep learning. This thesis is a response to that. It introduces the field of deep learning in a probabilistic machine learning setting for problems known from system identification.Our goal for sequential modeling within the scope of this thesis is to obtain a model with good predictive and/or generative capabilities. The motivation behind this is that such a model can then be used in other areas, such as control or reinforcement learning. The model could also be used as a stepping stone for machine learning problems or for pure recreational purposes.Paper I and Paper II focus on how to apply deep learning to common system identification problems. Paper I introduces a novel way of regularizing the impulse response estimator for a system. In contrast to previous methods using Gaussian processes for this regularization we propose to parameterize the regularization with a neural network and train this using a large dataset. Paper II introduces deep learning and many of its core concepts for a system identification audience. In the paper we also evaluate several contemporary deep learning models on standard system identification benchmarks. Paper III is the odd fish in the collection in that it focuses on the mathematical formulation and evaluation of calibration in classification especially for deep neural network. The paper proposes a new formalized notation for calibration and some novel ideas for evaluation of calibration. It also provides some experimental results on calibration evaluation.
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| 3. |
- Andersson Naesseth, Christian, et al.
(författare)
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High-Dimensional Filtering Using Nested Sequential Monte Carlo
- 2019
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Ingår i: IEEE Transactions on Signal Processing. - : IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC. - 1053-587X .- 1941-0476. ; 67:16, s. 4177-4188
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Tidskriftsartikel (refereegranskat)abstract
- Sequential Monte Carlo (SMC) methods comprise one of the most successful approaches to approximate Bayesian filtering. However, SMC without a good proposal distribution can perform poorly, in particular in high dimensions. We propose nested sequential Monte Carlo, a methodology that generalizes the SMC framework by requiring only approximate, properly weighted, samples from the SMC proposal distribution, while still resulting in a correctSMCalgorithm. This way, we can compute an "exact approximation" of, e. g., the locally optimal proposal, and extend the class of models forwhichwe can perform efficient inference using SMC. We showimproved accuracy over other state-of-the-art methods on several spatio-temporal state-space models.
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| 4. |
- Bijl, Hildo, et al.
(författare)
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Optimal controller/observer gains of discounted-cost LQG systems
- 2019
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Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 101, s. 471-474
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Tidskriftsartikel (refereegranskat)abstract
- The linear-quadratic-Gaussian (LQG) control paradigm is well-known in literature. The strategy of minimizing the cost function is available, both for the case where the state is known and where it is estimated through an observer. The situation is different when the cost function has an exponential discount factor, also known as a prescribed degree of stability. In this case, the optimal control strategy is only available when the state is known. This paper builds onward from that result, deriving an optimal control strategy when working with an estimated state. Expressions for the resulting optimal expected cost are also given.
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| 5. |
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| 6. |
- Dahlin, Johan, 1986-, et al.
(författare)
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Getting started with particle Metropolis-Hastings for inference in nonlinear dynamical models
- 2019
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Ingår i: Journal of Statistical Software. - Alexandria, VA, United States : American Statistical Association. - 1548-7660. ; 88:CN2, s. 1-41
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Tidskriftsartikel (refereegranskat)abstract
- This tutorial provides a gentle introduction to the particle Metropolis-Hastings (PMH) algorithm for parameter inference in nonlinear state-space models together with a software implementation in the statistical programming language R. We employ a step-by-step approach to develop an implementation of the PMH algorithm (and the particle filter within) together with the reader. This final implementation is also available as the package pmhtutorial in the CRAN repository. Throughout the tutorial, we provide some intuition as to how the algorithm operates and discuss some solutions to problems that might occur in practice. To illustrate the use of PMH, we consider parameter inference in a linear Gaussian state-space model with synthetic data and a nonlinear stochastic volatility model with real-world data.
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| 7. |
- Hostettler, Roland, et al.
(författare)
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Auxiliary-Particle-Filter-based Two-Filter Smoothing for Wiener State-Space Models
- 2018
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Ingår i: Proceedings of the 21st International Conference on Information Fusion, Cambridge, UK, July, 2018.. - 9780996452779 ; , s. 1904-1911
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Konferensbidrag (refereegranskat)abstract
- In this paper, we propose an auxiliary-particlefilter-based two-filter smoother for Wiener state-space models. The proposed smoother exploits the model structure in order to obtain an analytical solution for the backward dynamics, which is introduced artificially in other two-filter smoothers. Furthermore, Gaussian approximations to the optimal proposal density and the adjustment multipliers are derived for both the forward and backward filters. The proposed algorithm is evaluated and compared to existing smoothing algorithms in a numerical example where it is shown that it performs similarly to the state of the art in terms of the root mean squared error at lower computational cost for large numbers of particles.
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| 8. |
- Jacob, Pierre, et al.
(författare)
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Retracted article: Smoothing with Couplings of Conditional Particle Filters
- 2018
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Ingår i: Journal of the American Statistical Association. - : Taylor & Francis. - 0162-1459 .- 1537-274X.
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Tidskriftsartikel (refereegranskat)abstract
- In state space models, smoothing refers to the task of estimating a latent stochastic process given noisy measurements related to the process. We propose an unbiased estimator of smoothing expectations. The lack-of-bias property has methodological benefits: independent estimators can be generated in parallel, and confidence intervals can be constructed from the central limit theorem to quantify the approximation error. To design unbiased estimators, we combine a generic debiasing technique for Markov chains, with a Markov chain Monte Carlo algorithm for smoothing. The resulting procedure is widely applicable and we show in numerical experiments that the removal of the bias comes at a manageable increase in variance. We establish the validity of the proposed estimators under mild assumptions. Numerical experiments are provided on toy models, including a setting of highly-informative observations, and for a realistic Lotka-Volterra model with an intractable transition density.
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| 9. |
- Jidling, Carl
(författare)
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Tailoring Gaussian processes for tomographic reconstruction
- 2019
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- A probabilistic model reasons about physical quantities as random variables that can be estimated from measured data. The Gaussian process is a respected member of this family, being a flexible non-parametric method that has proven strong capabilities in modelling a wide range of nonlinear functions. This thesis focuses on advanced Gaussian process techniques; the contribution consist of practical methodologies primarily intended for inverse tomographic applications.In our most theoretical formulation, we propose a constructive procedure for building a customised covariance function given any set of linear constraints. These are explicitly incorporated in the prior distribution and thereby guaranteed to be fulfilled by the prediction.One such construction is employed for strain field reconstruction, to which end we successfully introduce the Gaussian process framework. A particularly well-suited spectral based approximation method is used to obtain a significant reduction of the computational load. The formulation has seen several subsequent extensions, represented in this thesis by a generalisation that includes boundary information and uses variational inference to overcome the challenge provided by a nonlinear measurement model.We also consider X-ray computed tomography, a field of high importance primarily due to its central role in medical treatments. We use the Gaussian process to provide an alternative interpretation of traditional algorithms and demonstrate promising experimental results. Moreover, we turn our focus to deep kernel learning, a special construction in which the expressiveness of a standard covariance function is increased through a neural network input transformation. We develop a method that makes this approach computationally feasible for integral measurements, and the results indicate a high potential for computed tomography problems.
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| 10. |
- Kok, Manon, et al.
(författare)
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A Fast and Robust Algorithm for Orientation Estimation Using Inertial Sensors
- 2019
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Ingår i: IEEE Signal Processing Letters. - : IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC. - 1070-9908 .- 1558-2361. ; 26:11, s. 1673-1677
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Tidskriftsartikel (refereegranskat)abstract
- We present a novel algorithm for online, real-time orientation estimation. Our algorithm integrates gyroscope data and corrects the resulting orientation estimate for integration drift using accelerometer and magnetometer data. This correction is computed, at each time instance, using a single gradient descent step with fixed step length. This fixed step length results in robustness against model errors, e.g., caused by large accelerations or by short-term magnetic field disturbances, which we numerically illustrate using Monte Carlo simulations. Our algorithm estimates a three-dimensional update to the orientation rather than the entire orientation itself. This reduces the computational complexity by approximately 1/3 with respect to the state of the art. It also improves the quality of the resulting estimates, specifically when the orientation corrections are large. We illustrate the efficacy of the algorithm using experimental data.
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| 11. |
- Murray, Lawrence, et al.
(författare)
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Automated learning with a probabilistic programming language: Birch
- 2018
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Ingår i: Annual Reviews in Control. - : Elsevier. - 1367-5788 .- 1872-9088. ; 46, s. 29-43
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Tidskriftsartikel (refereegranskat)abstract
- This work offers a broad perspective on probabilistic modeling and inference in light of recent advances in probabilistic programming, in which models are formally expressed in Turing-complete programming languages. We consider a typical workflow and how probabilistic programming languages can help to automate this workflow, especially in the matching of models with inference methods. We focus on two properties of a model that are critical in this matching: its structure—the conditional dependencies between random variables—and its form—the precise mathematical definition of those dependencies. While the structure and form of a probabilistic model are often fixed a priori, it is a curiosity of probabilistic programming that they need not be, and may instead vary according to random choices made during program execution. We introduce a formal description of models expressed as programs, and discuss some of the ways in which probabilistic programming languages can reveal the structure and form of these, in order to tailor inference methods. We demonstrate the ideas with a new probabilistic programming language called Birch, with a multiple object tracking example.
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| 12. |
- 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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| 13. |
- Osama, Muhammad, et al.
(författare)
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Inferring Heterogeneous Causal Effects in Presence of Spatial Confounding
- 2019
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Ingår i: Proceedings of the 36th International Conference on Machine Learning. ; , s. 4942-4950
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Konferensbidrag (refereegranskat)abstract
- We address the problem of inferring the causal effect of an exposure on an outcome across space, using observational data. The data is possibly subject to unmeasured confounding variables which, in a standard approach, must be adjusted for by estimating a nuisance function. Here we develop a method that eliminates the nuisance function, while mitigating the resulting errors-in-variables. The result is a robust and accurate inference method for spatially varying heterogeneous causal effects. The properties of the method are demonstrated on synthetic as well as real data from Germany and the US.
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| 14. |
- Ribeiro, Antonio, et al.
(författare)
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Automatic diagnosis of short-duration 12-lead ECG using a deep convolutional network
- 2018
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Ingår i: <em>ML4H: Machine Learning for Health Workshop at NeurIPS</em>, Montréal, Canada, December 2018..
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Konferensbidrag (refereegranskat)abstract
- We present a model for predicting electrocardiogram (ECG) abnormalities in shortduration 12-lead ECG signals which outperformed medical doctors on the 4th year of their cardiology residency. Such exams can provide a full evaluation of heart activity and have not been studied in previous end-to-end machine learning papers. Using the database of a large telehealth network, we built a novel dataset with more than 2 million ECG tracings, orders of magnitude larger than those used in previous studies. Moreover, our dataset is more realistic, as it consist of 12-lead ECGs recorded during standard in-clinics exams. Using this data, we trained a residual neural network with 9 convolutional layers to map 7 to 10 second ECG signals to 6 classes of ECG abnormalities. Future work should extend these results to cover a large range of ECG abnormalities, which could improve the accessibility of this diagnostic tool and avoid wrong diagnosis from medical doctors.
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| 15. |
- Rogers, T J, et al.
(författare)
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Identification of a Duffing oscillator using particle Gibbs with ancestor sampling
- 2019
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Ingår i: Journal of Physics, Conference Series. - : Institute of Physics Publishing (IOPP). - 1742-6588 .- 1742-6596. ; 1264:1
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Tidskriftsartikel (refereegranskat)abstract
- The Duffing oscillator remains a key benchmark in nonlinear systems analysis and poses interesting challenges in nonlinear structural identification. The use of particle methods or sequential Monte Carlo (SMC) is becoming a more common approach for tackling these nonlinear dynamical systems, within structural dynamics and beyond. This paper demonstrates the use of a tailored SMC algorithm within a Markov Chain Monte Carlo (MCMC) scheme to allow inference over the latent states and parameters of the Duffing oscillator in a Bayesian manner. This approach to system identification offers a statistically more rigorous treatment of the problem than the common state-augmentation methods where the parameters of the model are included as additional latent states. It is shown how recent advances in particle MCMC methods, namely the particle Gibbs with ancestor sampling (PG-AS) algorithm is capable of performing efficient Bayesian inference, even in cases where little is known about the system parameters a priori. The advantage of this Bayesian approach is the quantification of uncertainty, not only in the system parameters but also in the states of the model (displacement and velocity) even in the presence of measurement noise.
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| 16. |
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| 17. |
- Svensson, Andreas, et al.
(författare)
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Computationally Efficient Bayesian Learning of Gaussian Process State Space Models
- 2016
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Ingår i: Proceedings of the 19th International Conference on Artificial Intelligence and Statistics. ; , s. 213-221
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Konferensbidrag (refereegranskat)abstract
- Gaussian processes allow for flexible specification of prior assumptions of unknown dynamics in state space models. We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is formed by projecting the problem onto a set of approximate eigenfunctions derived from the prior covariance structure. Learning under this family of models can be conducted using a carefully crafted particle MCMC algorithm. This scheme is computationally efficient and yet allows for a fully Bayesian treatment of the problem. Compared to conventional system identification tools or existing learning methods, we show competitive performance and reliable quantification of uncertainties in the model.
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| 18. |
- Taghia, Jalil, et al.
(författare)
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Conditionally Independent Multiresolution Gaussian Processes
- 2019
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Ingår i: 22nd International Conference On Artificial Intelligence And Statistics, Vol 89.
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Konferensbidrag (refereegranskat)abstract
- The multiresolution Gaussian process (GP) has gained increasing attention as a viable approach towards improving the quality of approximations in GPs that scale well to large-scale data. Most of the current constructions assume full independence across resolutions. This assumption simplifies the inference, but it underestimates the uncertainties in transitioning from one resolution to another. This in turn results in models which are prone to overfitting in the sense of excessive sensitivity to the chosen resolution, and predictions which are non-smooth at the boundaries. Our contribution is a new construction which instead assumes conditional independence among GPs across resolutions. We show that relaxing the full independence assumption enables robustness against overfitting, and that it delivers predictions that are smooth at the boundaries. Our new model is compared against current state of the art on 2 synthetic and 9 real-world datasets. In most cases, our new conditionally independent construction performed favorably when compared against models based on the full independence assumption. In particular, it exhibits little to no signs of overfitting.
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| 19. |
- Umenberger, Jack, et al.
(författare)
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Bayesian identification of state-space models via adaptive thermostats
- 2019
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Ingår i: 2019 IEEE 58th conference on decision and control (CDC). - : IEEE. - 9781728113982 ; , s. 7382-7388
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Konferensbidrag (refereegranskat)abstract
- Bayesian modeling has been recognized as a powerful approach to system identification, not least due to its intrinsic uncertainty quantification. However, despite many recent developments, Bayesian identification of nonlinear state space models still poses major computational challenges. We propose a new method to tackle this problem. The technique is based on simulating a so-called thermostat, a stochastic differential equation constructed to have the posterior parameter distribution as its limiting distribution. Simulating the thermostat requires access to unbiased estimates of the gradient of the log-posterior. To handle this, we make use of a recent method for debiasing particle-filter-based smoothing estimates. Numerical results show a clear benefit of this approach compared to a direct application of (biased) particle-filter-based gradient estimates within the thermostat.
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| 20. |
- Umenberger, Jack, et al.
(författare)
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Learning convex bounds for linear quadratic control policy synthesis
- 2018
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Ingår i: Neural Information Processing Systems 2018.
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Konferensbidrag (refereegranskat)abstract
- Learning to make decisions from observed data in dynamic environments remains a problem of fundamental importance in a numbers of fields, from artificial intelligence and robotics, to medicine and finance. This paper concerns the problem of learning control policies for unknown linear dynamical systems so as to maximize a quadratic reward function. We present a method to optimize the expected value of the reward over the posterior distribution of the unknown system parameters, given data. The algorithm involves sequential convex programing, and enjoys reliable local convergence and robust stability guarantees. Numerical simulations and stabilization of a real-world inverted pendulum are used to demonstrate the approach, with strong performance and robustness properties observed in both.
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| 21. |
- Umenberger, Jack, et al.
(författare)
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Robust exploration in linear quadratic reinforcement learning
- 2019
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Ingår i: Advances in neural information processing systems 32 (NIPS 2019). - : Neural Information Processing Systems (NIPS). ; , s. 15310-15320
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Konferensbidrag (refereegranskat)abstract
- This paper concerns the problem of learning control policies for an unknown linear dynamical system to minimize a quadratic cost function. We present a method, based on convex optimization, that accomplishes this task robustly: i.e., we minimize the worst-case cost, accounting for system uncertainty given the observed data. The method balances exploitation and exploration, exciting the system in such a way so as to reduce uncertainty in the model parameters to which the worst-case cost is most sensitive. Numerical simulations and application to a hardware-in-the-loop servo-mechanism demonstrate the approach, with appreciable performance and robustness gains over alternative methods observed in both.
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| 22. |
- Valenzuela, Patricio E., et al.
(författare)
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On model order priors for Bayesian identification of SISO linear systems
- 2019
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Ingår i: International Journal of Control. - : Taylor & Francis. - 0020-7179 .- 1366-5820. ; 92:7, s. 1645-1661
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Tidskriftsartikel (refereegranskat)abstract
- A method for the identification of single input single output linear systems is presented. The method employs a Bayesian approach to compute the posterior distribution of the model parameters given the data-set. Since this distribution is often unavailable in closed form, a Metropolis Hastings algorithm is implemented to draw samples from it. To implement the sampler, the inclusion of prior information regarding the model order of the identified system is discussed. As one of the main contributions of this work, a prior over the Hankel singular values of the model is imposed. Numerical examples illustrate the method.
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| 23. |
- Wågberg, Johan, et al.
(författare)
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Regularized parametric system identification : a decision-theoretic formulation
- 2018
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Ingår i: 2018 Annual American Control Conference (ACC). - : IEEE. - 9781538654286 - 9781538654279 - 9781538654293 ; , s. 1895-1900
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Konferensbidrag (refereegranskat)abstract
- Parametric prediction error methods constitute a classical approach to the identification of linear dynamic systems with excellent large-sample properties. A more recent regularized approach, inspired by machine learning and Bayesian methods, has also gained attention. Methods based on this approach estimate the system impulse response with excellent small-sample properties. In several applications, however, it is desirable to obtain a compact representation of the system in the form of a parametric model. By viewing the identification of such models as a decision, we develop a decision-theoretic formulation of the parametric system identification problem that bridges the gap between the classical and regularized approaches above. Using the output-error model class as an illustration, we show that this decision-theoretic approach leads to a regularized method that is robust to small sample-sizes as well as overparameterization.
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