Outlier robust system identification: a Bayesian kernel-based approach

Bottegal, Giulio; Aravkin, Aleksandr Y.; Hjalmarsson, Håkan; Pillonetto, Gianluigi

doi:10.3182/20140824-6-za-1003.01587

Cited by 10 publications

(8 citation statements)

References 24 publications

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“…In the system identification context, some out-lier robust methods have been developed in recent years [25,34,4,36]. In particular, [15,8] use non-Gaussian descriptions of noise, while [5] describes a computational framework based on interior point methods. In comparison with all these papers, the novelty of this work is to combine kernel-based approaches, noise mixture representations and EM techniques, to derive a new efficient estimator of the impulse response and kernel/noise hyperparameters.…”

Section: Statement Of Contribution and Organization Of The Papermentioning

confidence: 99%

“…All of these subproblems, except one involving a parameter connected with the dominant pole of the system, can be solved in parallel and admit a closed-form solution. This makes the proposed method computationally attractive, especially when compared to possible alternative solutions such as approximate Bayesian methods (e.g., Expectation Propagation [24] and Variational Bayes [6]), or full Bayesian methods [8].…”

Section: Statement Of Contribution and Organization Of The Papermentioning

confidence: 99%

“…In (8), Σ v represents the covariance matrix of the noise vector v; in this case we have Σ v = σ 2 I N . Equation ( 7) is instrumental to derive our impulse response estimator, which can be obtained as its minimum mean square error (MSE) (or Bayesian) estimate [2] ĝ = E[g|y, λ, β] = Cy .…”

Section: The Stable Spline Kernel and System Identification Under Gau...mentioning

confidence: 99%

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Robust EM kernel-based methods for linear system identification

et al. 2016

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Recent developments in system identification have brought attention to regularized kernel-based methods. This type of approach has been proven to compare favorably with classic parametric methods. However, current formulations are not robust with respect to outliers. In this paper, we introduce a novel method to robustify kernel-based system identification methods. To this end, we model the output measurement noise using random variables with heavy-tailed probability density functions (pdfs), focusing on the Laplacian and the Student's t distributions. Exploiting the representation of these pdfs as scale mixtures of Gaussians, we cast our system identification problem into a Gaussian process regression framework, which requires estimating a number of hyperparameters of the data size order. To overcome this difficulty, we design a new maximum a posteriori (MAP) estimator of the hyperparameters, and solve the related optimization problem with a novel iterative scheme based on the Expectation-Maximization (EM) method. In presence of outliers, tests on simulated data and on a real system show a substantial performance improvement compared to currently used kernel-based methods for linear system identification.

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Section: Statement Of Contribution and Organization Of The Papermentioning

confidence: 99%

Section: Statement Of Contribution and Organization Of The Papermentioning

confidence: 99%

Section: The Stable Spline Kernel and System Identification Under Gau...mentioning

confidence: 99%

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Robust EM kernel-based methods for linear system identification

et al. 2016

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“…Reference [26] introduced a mixed model of multivariate Gauss distribution and multivariate Uniform distribution, and applied it to clustering and classification of models, in which the validity of the mixed model was shown. In reference [27], a linear system identification method based on abnormal robust regular kernel was proposed. Unknown variables were modeled into Gauss processes, and noise signals were modeled into Laplace random variables, which improves the robustness of the system.…”

Section: Introductionmentioning

confidence: 99%

Mixed Probability Inverse Depth Estimation Based on Probabilistic Graph Model

Liu

Wang

et al. 2019

IEEE Access

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In this paper, a mixed probability inverse depth estimation method based on probabilistic graph model is proposed, which can effectively solve the problems of far distance from the camera center and long data tail in depth estimation. At the same time, not only the accuracy can be improved but also the robustness of inverse depth estimation can be developed. First, the triangle method was used to find the depth information and location of a point in space, and the inverse depth information was obtained as the initial information of inverse depth estimation. Then, the basic matrix in epipolar geometry was obtained by using the normalized eight-point algorithm, and the pose of a camera was obtained as the initial information of optimization. Next, the pose of the monocular camera was modeled by a factor graph model, and the pose estimation was transformed into an unconstrained optimization problem by using the transformation relationship between Lie group and Lie algebra to obtain the pose of the camera. Finally, the inverse depth obtained by using the Gauss-uniform mixed probability distribution based on the probability graph model was used to calculate the recurrence formula by approximate inference, which can facilitate the sequential processing of multiple images. The depth information was quantitatively measured and compared by using TUM datasets, and the length of space object was measured by using inverse depth information, thus the measurement accuracy of this method was indirectly verified. This method is characterized by strong robustness and high measurement accuracy in the environments with random interferences. INDEX TERMS Mixed probability distribution model, factor graph, inverse depth estimation, Lie group and Lie algebra, fundamental matrix, camera pose.

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“…The main advantage of the Gibbs sampler is that it does not require any rejection criterion of the generated samples and quickly converges to the target distribution. Note that MCMC-based approaches have recently gained popularity in system identification [Ninness and Henriksen, 2010], [Lindsten et al, 2012], [Bottegal et al, 2014].…”

Section: Introductionmentioning

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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Outlier robust system identification: a Bayesian kernel-based approach

Cited by 10 publications

References 24 publications

Robust EM kernel-based methods for linear system identification

Robust EM kernel-based methods for linear system identification

Mixed Probability Inverse Depth Estimation Based on Probabilistic Graph Model

Bayesian kernel-based system identification with quantized output data

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