Regularized spectrum estimation using stable spline kernels

Bottegal, Giulio; Pillonetto, Gianluigi

doi:10.1016/j.automatica.2013.08.010

Cited by 13 publications

(22 citation statements)

References 18 publications

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“…The estimation procedure of β is in a certain sense "non-optimal", since it is based on a different noise model. However, we observe that the sensitivity of the estimator to the value of β is relatively low, in the sense that a large interval of values of β can model a given realization of g efficiently (see Lemma 2 in [Bottegal and Pillonetto, 2013]). Models for β will be introduced in future works.…”

Section: = Limmentioning

confidence: 99%

Outlier robust system identification: a Bayesian kernel-based approach

Bottegal

Aravkin

Hjalmarsson

et al. 2014

IFAC Proceedings Volumes

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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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Section: = Limmentioning

confidence: 99%

Outlier robust system identification: a Bayesian kernel-based approach

Bottegal

Aravkin

Hjalmarsson

et al. 2014

IFAC Proceedings Volumes

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“…In this context, K β is usually called a kernel and determines the properties of the realizations of g. In this paper, we choose K β from the family of stable spline kernels [Pillonetto and De Nicolao, 2010], [Pillonetto et al, 2011]. Such kernels are specifically designed for system identification purposes and give clear advantages compared to other standard kernels [Bottegal and Pillonetto, 2013], [Pillonetto and De Nicolao, 2010] (like the quadratic kernel or the Laplacian kernel, see [Schölkopf and Smola, 2001]). In this paper we make use of the first-order stable spline kernel (or TC kernel in [Chen et al, 2012a]).…”

Section: Establishing a Prior For The Systemmentioning

confidence: 99%

Bayesian kernel-based system identification with quantized output data

2015

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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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“…To this end, we model the impulse response of the unknown system as a realization of a zero-mean Gaussian random process. The covariance matrix (in this context also called a kernel ) corresponds to the recently introduced stable spline kernel (see [34], [33], [4]). The structure of this type of kernel depends on two hyperparameters, that need to be estimated from data.…”

Section: Introductionmentioning

confidence: 99%

A new kernel-based approach to system identification with quantized output data

2017

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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 methods to provide an estimate of the system. In particular, we design two methods based on the so-called Gibbs sampler that allow also to estimate the kernel hyperparameters by marginal likelihood maximization via the expectation-maximization method. Numerical simulations show the effectiveness of the proposed scheme, as compared to the state-of-the-art kernel-based methods when these are employed in system identification with quantized data.

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Regularized spectrum estimation using stable spline kernels

Cited by 13 publications

References 18 publications

Outlier robust system identification: a Bayesian kernel-based approach

Outlier robust system identification: a Bayesian kernel-based approach

Bayesian kernel-based system identification with quantized output data

A new kernel-based approach to system identification with quantized output data

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