| 1. |
- Bottegal, Giulio, et al.
(författare)
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Bayesian kernel-based system identification with quantized output data
- 2015
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Ingår i: IFAC-PapersOnLine. - : Elsevier. - 2405-8963. ; 48:28, s. 455-460
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we introduce a novel method for linear system identification with quantized output data. We model the impulse response as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential stability. This serves as a starting point to cast our system identification problem into a Bayesian framework. We employ Markov Chain Monte Carlo (MCMC) methods to provide an estimate of the system. In particular, we show how to design a Gibbs sampler which quickly converges to the target distribution. Numerical simulations show a substantial improvement in the accuracy of the estimates over state-of-the-art kernel-based methods when employed in identification of systems with quantized data.
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| 2. |
- Bottegal, Giulio, et al.
(författare)
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Outlier robust kernel-based system identification using l1-Laplace techniques
- 2015
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Ingår i: 2015 54th IEEE Conference on Decision and Control. - : Institute of Electrical and Electronics Engineers (IEEE). ; , s. 2109-2114
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Konferensbidrag (refereegranskat)abstract
- Regularized kernel-based methods for system identification have gained popularity in recent years. However, current formulations are not robust with respect to outliers. In this paper, we study possible solutions to robustify kernel-based methods that rely on modeling noise using the Laplacian probability density function (pdf). The contribution of this paper is two-fold. First, we introduce a new outlier robust kernel-based system identification method. It exploits the representation of Laplacian pdfs as scale mixture of Gaussians. The hyperparameters characterizing the problem are chosen using a new maximum a posteriori estimator whose solution is computed using a novel iterative scheme based on the expectation-maximization method. The second contribution of the paper is the review of two other robust kernel-based methods. The three methods are compared by means of numerical experiments, which show that all of them give substantial performance improvements compared to standard kernel-based methods for linear system identification.
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| 3. |
- Bottegal, Giulio, et al.
(författare)
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Outlier robust system identification : A Bayesian kernel-based approach
- 2014
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Ingår i: IFAC Proceedings Volumes (IFAC-PapersOnline). - : IFAC Papers Online. - 9783902823625 ; , s. 1073-1078
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Konferensbidrag (refereegranskat)abstract
- In this paper, we propose an outlier-robust regularized kernel-based method for linear system identification. The unknown impulse response is modeled as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential stability. To build robustness to outliers, we model the measurement noise as realizations of independent Laplacian random variables. The identification problem is cast in a Bayesian framework, and solved by a new Markov Chain Monte Carlo (MCMC) scheme. In particular, exploiting the representation of the Laplacian random variables as scale mixtures of Gaussians, we design a Gibbs sampler which quickly converges to the target distribution. Numerical simulations show a substantial improvement in the accuracy of the estimates over state-of-the-art kernel-based methods.
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| 4. |
- Del Favero, S., et al.
(författare)
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Bayesian learning of probability density functions : A Markov chain Monte Carlo approach
- 2012
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Ingår i: Decision and Control (CDC), 2012 IEEE 51st Annual Conference on. - : IEEE. ; , s. 1512-1517
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Konferensbidrag (refereegranskat)abstract
- The paper considers the problem of reconstructing a probability density function from a finite set of samples independently drawn from it.We cast the problem in a Bayesian setting where the unknown density is modeled via a nonlinear transformation of a Bayesian prior placed on a Reproducing Kernel Hilbert Space. The learning of the unknown density function is then formulated as a minimum variance estimation problem. Since this requires the solution of analytically intractable integrals, we solve this problem by proposing a novel algorithm based on the Markov chain Monte Carlo framework. Simulations are used to corroborate the goodness of the new approach.
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| 5. |
- Pillonetto, G., et al.
(författare)
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Full Bayesian identification of linear dynamic systems using stable kernels
- 2023
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Ingår i: Proceedings of the National Academy of Sciences of the United States of America. - : NATL ACAD SCIENCES. - 0027-8424 .- 1091-6490. ; 120:18
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Tidskriftsartikel (refereegranskat)abstract
- System identification learns mathematical models of dynamic systems starting from input-output data. Despite its long history, such research area is still extremely active. New challenges are posed by identification of complex physical processes given by the interconnection of dynamic systems. Examples arise in biology and industry, e.g., in the study of brain dynamics or sensor networks. In the last years, regularized kernel-based identification, with inspiration from machine learning, has emerged as an interesting alternative to the classical approach commonly adopted in the literature. In the linear setting, it uses the class of stable kernels to include fundamental features of physical dynamical systems, e.g., smooth exponential decay of impulse responses. Such class includes also unknown continuous parameters, called hyperparameters, which play a similar role as the model discrete order in controlling complexity. In this paper, we develop a linear system identification procedure by casting stable kernels in a full Bayesian framework. Our models incorporate hyperparameters uncertainty and consist of a mixture of dynamic systems over a continuum spectrum of dimensions. They are obtained by overcoming drawbacks related to classical Markov chain Monte Carlo schemes that, when applied to stable kernels, are proved to become nearly reducible (i.e., unable to reconstruct posteriors of interest in reasonable time). Numerical experiments show that full Bayes frequently outperforms the state-of-the-art results on typical benchmark problems. Two real applications related to brain dynamics (neural activity) and sensor networks are also included.
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| 6. |
- Varagnolo, Damiano, et al.
(författare)
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Distributed parametric and nonparametric regression with on-line performance bounds computation
- 2012
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Ingår i: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 48:10, s. 2468-2481
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we focus on collaborative multi-agent systems, where agents are distributed over a region of interest and collaborate to achieve a common estimation goal. In particular, we introduce two consensus-based distributed linear estimators. The first one is designed for a Bayesian scenario, where an unknown common finite-dimensional parameter vector has to be reconstructed, while the second one regards the nonparametric reconstruction of an unknown function sampled at different locations by the sensors. Both of the algorithms are characterized in terms of the trade-off between estimation performance, communication, computation and memory complexity. In the finite-dimensional setting, we derive mild sufficient conditions which ensure that a distributed estimator performs better than the local optimal ones in terms of estimation error variance. In the nonparametric setting, we introduce an on-line algorithm that allows the agents to simultaneously compute the function estimate with small computational, communication and data storage efforts, as well as to quantify its distance from the centralized estimate given by a Regularization Network, one of the most powerful regularized kernel methods. These results are obtained by deriving bounds on the estimation error that provide insights on how the uncertainty inherent in a sensor network, such as imperfect knowledge on the number of agents and the measurement models used by the sensors, can degrade the performance of the estimation process. Numerical experiments are included to support the theoretical findings.
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| 7. |
- Zanella, F., et al.
(författare)
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Asynchronous Newton-Raphson Consensus for distributed convex optimization
- 2012
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Ingår i: Estimation and Control of Networked Systems. - 9783902823229 ; , s. 133-138
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Konferensbidrag (refereegranskat)abstract
- We consider the distributed unconstrained minimization of separable convex cost functions, where the global cost is given by the sum of several local and private costs, each associated to a specific agent of a given communication network. We specifically address an asynchronous distributed optimization technique called Newton-Raphson Consensus. Beside having low computational complexity, low communication requirements and being interpretable as a distributed Newton-Raphson algorithm, the technique has also the beneficial properties of requiring very little coordination and naturally supporting time-varying topologies. In this work we analytically prove that under some assumptions it shows either local or global convergence properties, and corroborate this result by the means of numerical simulations.
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