Relevance singular vector machine for low-rank matrix sensing

Sundin, Martin; Chatterjee, Saikat; Jansson, Magnus; Rojas, Cristian R.

doi:10.1109/spcom.2014.6983925

Cited by 6 publications

(6 citation statements)

References 14 publications

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“…A "general" form (see Wipf (2012); Prando et al (2014)) of a low-rank promoting prior for a matrix A, which involves quadratic forms of A, has the structure p λ (A) ∝ e −λT r(QAA ⊤ ) (62) where Q = Q ⊤ ≥ 0 plays the role of an hyperparameter. Slightly different structures have been proposed in Sundin et al (2014) where "left" and "right" hyperparameters have been considered.…”

Section: Low Mcmillan Degree Hankel Matrices and Sparsitymentioning

confidence: 99%

Regularization and Bayesian learning in dynamical systems: Past, present and future

Chiuso

2016

Annual Reviews in Control

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Regularization and Bayesian methods for system identification have been repopularized in the recent years, and proved to be competitive w.r.t. classical parametric approaches. In this paper we shall make an attempt to illustrate how the use of regularization in system identification has evolved over the years, starting from the early contributions both in the Automatic Control as well as Econometrics and Statistics literature. In particular we shall discuss some fundamental issues such as compound estimation problems and exchangeability which play and important role in regularization and Bayesian approaches, as also illustrated in early publications in Statistics. The historical and foundational issues will be given more emphasis (and space), at the expense of the more recent developments which are only briefly discussed. The main reason for such a choice is that, while the recent literature is readily available, and surveys have already been published on the subject, in the author's opinion a clear link with past work had not been completely clarified.

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Section: Low Mcmillan Degree Hankel Matrices and Sparsitymentioning

confidence: 99%

Regularization and Bayesian learning in dynamical systems: Past, present and future

Chiuso

2016

Annual Reviews in Control

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“…The Wishart distribution is a conjugate prior for a one-sided precision and is closely related to the sparsity promoting Gamma prior used by the relevance vector machine (RVM) [15] and in sparse Bayesian learning [16,17]. Motivated by the conceptual similarity of RVM, we used the name relevance singular vector machine (RSVM) in [12] where the prior (2) was used for low-rank matrix estimation from linear measurements. The method in this paper is an outlier robust version of the RSVM for the RPCA model (1), therefore we refer to the new method as robust RSVM (rRSVM).…”

Section: Low-rank Promoting Priormentioning

confidence: 99%

“…To promote low-rank, we use a model that induces correlations among the column and row vectors of X. The low-rank prior was first introduced by us in [12], where the Bayesian learning method was named relevance singular vector machine (RSVM) in [12]. The RSVM was not investigated for robustness against sparse outliers.…”

Section: Introductionmentioning

confidence: 99%

“…Further, for typical sparse representations (for example compressed sensing), we experienced in [13] that a combined model of the sparse and dense noise works better than treating the noise terms independently. In this paper, we investigate the Bayesian modeling of the RPCA problem (1) using a combined model for S + N and the low-rank promoting prior from [12]. The new method is called robust RSVM (rRSVM) and the parameters are estimated using the expectation-maximization (EM) framework.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian learning for robust principal component analysis

Sundin

Chatterjee

Jansson

2015

2015 23rd European Signal Processing Conference (EUSIPCO)

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We develop a Bayesian learning method for robust principal component analysis where the main task is to estimate a low-rank matrix from noisy and outlier contaminated measurements. To promote low-rank, we use a structured Gaussian prior that induces correlations among column vectors as well as row vectors of the matrix under estimation. In our method, the noise and outliers are modeled by a combined noise model. The method is evaluated and compared to other methods using synthetic data as well as data from the MovieLens 100K dataset. Comparisons show that the method empirically provides a significant performance improvement over existing methods.

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“…Parts of this paper was presented at the International Conference on Signal Processing and Communications (SPCOM), July 2014, Bangalore, India [37].…”

Section: Introductionmentioning

confidence: 99%

Relevance Singular Vector Machine for Low-Rank Matrix Reconstruction

Sundin

Rojas

Jansson

et al. 2016

IEEE Trans. Signal Process.

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We develop Bayesian learning methods for lowrank matrix reconstruction and completion from linear measurements. For under-determined systems, the developed methods reconstruct low-rank matrices when neither the rank nor the noise power is known a-priori. We derive relations between the proposed Bayesian models and low-rank promoting penalty functions. The relations justify the use of Kronecker structured covariance matrices in a Gaussian based prior. In the methods, we use expectation-maximization to learn the model parameters. The performance of the methods is evaluated through extensive numerical simulations on synthetic and real data.

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Relevance singular vector machine for low-rank matrix sensing

Cited by 6 publications

References 14 publications

Regularization and Bayesian learning in dynamical systems: Past, present and future

Regularization and Bayesian learning in dynamical systems: Past, present and future

Bayesian learning for robust principal component analysis

Relevance Singular Vector Machine for Low-Rank Matrix Reconstruction

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