Robust rank constrained kronecker covariance matrix estimation

Breloy, Arnaud; Sun, Yan; Babu, Prabhu; Ginolhac, Guillaume; Palomar, Daniel P.

doi:10.1109/acssc.2016.7869159

Cited by 7 publications

(10 citation statements)

References 18 publications

(28 reference statements)

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“…. , y N (could be any consistent estimator of R e up to a scale factor, e.g., R = R m ) 3: Return: µ SESAME by minimizing J Rm, R (µ) (See (13) or (14). )…”

Section: Algorithm 1 Sesamementioning

confidence: 99%

“…The pseudo-true parameter vector, µ 0 , is equal to µ c . Thus, the SESAME estimate, µ, given by (13), is a consistent estimator of µ 0 such that…”

Section: Corollarymentioning

confidence: 99%

“…In some practical applications, performance is degraded because the assumption of Gaussian distribution leads to nonrobustness, either to heavy-tailed distributed data or to outliers in the sample set. In order to overcome this issue, a wide class of distribution free methods based on the unstructured Tyler's estimate has been proposed [11,12,13,14]. Those methods begin by normalizing the zero mean observations to get rid of the potential power fluctuations.…”

Section: Introductionmentioning

confidence: 99%

“…Specifically, in [11], a robust extension of the COvariance Matching Estimation Technique (COMET) procedure is derived. In [12,13], estimators have been proposed which minimize a constrained version of Tyler's cost function using iterative Majorization-Minimization algorithms. In [14], a COnvexly ConstrAined (COCA) CM estimator is presented, based on the generalized Method of Moments (MoM) for Tyler's estimate subject to convex constraints.…”

Section: Introductionmentioning

confidence: 99%

“…The SESAME estimate, µ, given by(13), is a consistent estimator of µ c such that vec (R (µ c )) = r c σ −1 r e = σ −1 vec (R (µ e )). Likewise, R ( µ) is a consistent estimator of σ −1 R (µ e ).…”

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confidence: 99%

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Robust estimation of structured scatter matrices in (mis)matched models

et al. 2019

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Covariance matrix estimation is a ubiquitous problem in signal processing. In most modern signal processing applications, data are generally modeled by non-Gaussian distributions with covariance matrices exhibiting a particular structure. Taking into account this structure and the non-Gaussian behavior improve drastically the estimation accuracy. In this paper, we consider the estimation of structured scatter matrix for complex elliptically distributed observations, where the assumed model can differ from the actual distribution of the observations. Specifically, we tackle this problem, in a mismatched framework, by proposing a novel estimator, named StructurEd ScAtter Matrix Estimator (SESAME), which is based on a two-step estimation procedure. We conduct theoretical analysis on the unbiasedness and the asymptotic efficiency and Gaussianity of SESAME. In addition, we derive a recursive estimation procedure that iteratively applies the SESAME method, called Recursive-SESAME (R-SESAME), reaching with improved performance at lower sample support the (Mismatched) Cramér-Rao Bound. Furthermore, we show that some special cases of the proposed method allow to retrieve preexisting methods. Finally, numerical results corroborate the theoretical analysis and assess the usefulness of the proposed algorithms.

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“…. , y N (could be any consistent estimator of R e up to a scale factor, e.g., R = R m ) 3: Return: µ SESAME by minimizing J Rm, R (µ) (See (13) or (14). )…”

Section: Algorithm 1 Sesamementioning

confidence: 99%

“…The pseudo-true parameter vector, µ 0 , is equal to µ c . Thus, the SESAME estimate, µ, given by (13), is a consistent estimator of µ 0 such that…”

Section: Corollarymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Robust estimation of structured scatter matrices in (mis)matched models

et al. 2019

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Joint Learning of Full-structure Noise in Hierarchical Bayesian Regression Models

Hashemi

Cai

Gao

et al. 2021

Preprint

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We consider the reconstruction of brain activity from electroencephalography (EEG). This inverse problem can be formulated as a linear regression with independent Gaussian scale mixture priors for both the source and noise components. Crucial factors influencing accuracy of source estimation are not only the noise level but also its correlation structure, but existing approaches have not addressed estimation of noise covariance matrices with full structure. To address this shortcoming, we develop hierarchical Bayesian (type-II maximum likelihood) models for observations with latent variables for source and noise, which are estimated jointly from data. As an extension to classical sparse Bayesian learning (SBL), where across-sensor observations are assumed to be independent and identically distributed, we consider Gaussian noise with full covariance structure. Using the majorization-maximization framework and Riemannian geometry, we derive an efficient algorithm for updating the noise covariance along the manifold of positive definite matrices. We demonstrate that our algorithm has guaranteed and fast convergence and validate it in simulations and with real MEG data. Our results demonstrate that the novel framework significantly improves upon state-of-the-art techniques in the real-world scenario where the noise is indeed non-diagonal and fully-structured. Our method has applications in many domains beyond biomagnetic inverse problems.

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