Group-sparse regression using the covariance fitting criterion

Kronvall, Ted; Adalbjrnsson, Stefan Ingi; Nadig, Santhosh; Jakobsson, Andreas

doi:10.1016/j.sigpro.2017.03.025

Cited by 19 publications

(6 citation statements)

References 46 publications

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“…See [21], [22] for a detailed discussion about the similarities and differences of some of these methods. Many of these algorithms have been extended to include a group structure, such as the group-LASSO [23]- [26], blockwise sparse regression [27], block matching pursuit [28], group-SBL [29], [30], patterncoupled SBL [31] and group-SPICE [32]. A disadvantage of using a fixed dictionary matrix is the spectral leakage induced by the model mismatch, which decreases the estimation performance [33], [34].…”

Section: A State Of the Artmentioning

confidence: 99%

Variational Inference of Structured Line Spectra Exploiting Group-Sparsity

Möderl¹,

Pernkopf²,

Witrisal³

et al. 2023

Preprint

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In this paper, we present a variational inference algorithm that decomposes a signal into multiple groups of related spectral lines. The spectral lines in each group are associated with a group parameter common to all spectral lines within the group. The proposed algorithm jointly estimates the group parameters, the number of spetral lines within a group, and the number of groups exploiting a Bernoulli-Gamma-Gaussian hierarchical prior model which promotes sparse solutions. Aiming to maximize the evidence lower bound (ELBO), variational inference provides analytic approximations of the posterior probability density functions (PDFs) and also gives estimates of the additional model parameters such as the measurement noise variance. While the activation variables of the groups and the associated group parameters (such as fundamental frequencies and the corresponding higher order harmonics) are estimated as point estimates, the remaining parameters such as the complex amplitudes of the spectral lines and their precision parameters are estimated as approximate posterior PDFs.We demonstrate the versatility and performance of the proposed algorithm on three different inference problems. In particular, the proposed algorithm is applied to the multipitch estimation problem, the radar signal-based extended object estimation problem, and variational mode decomposition (VMD) using synthetic measurements and to real multi-pitch estimation problem using the Bach-10 dataset. The results show that the proposed algorithm outperforms state-of-the-art model-based and pre-trained algorithms on all three inference problems.

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Section: A State Of the Artmentioning

confidence: 99%

Variational Inference of Structured Line Spectra Exploiting Group-Sparsity

Möderl¹,

Pernkopf²,

Witrisal³

et al. 2023

Preprint

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“…They are (a) single measurement vector (SMV), (b) block single measurement vector (BSMV), (c) multiple measurement vector (MMV) and (d) block multiple measurement vector (BMMV). For example, as mentioned in [31], SMV models are used in wireless signal detection [33], MMV models in Electroencephalogram (EEG) [34], BSMV models in multi pitch estimation [35] and BMMV models in face recognition [36]. Here, we consider the BMMV model, since it is the general setting and the rest of the models are special cases of BMMV.…”

Section: Problem Statementmentioning

confidence: 99%

Model Selection in High-Dimensional Block-Sparse Linear Regression

Gohain¹,

Jansson²

2022

Preprint

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Model selection is an indispensable part of data analysis dealing very frequently with fitting and prediction purposes. In this paper, we tackle the problem of model selection in a general linear regression where the parameter matrix possesses a block-sparse structure, i.e., the non-zero entries occur in clusters or blocks and the number of such non-zero blocks is very small compared to the parameter dimension. Furthermore, a high-dimensional setting is considered where the parameter dimension is quite large compared to the number of available measurements. To perform model selection in this setting, we present an information criterion that is a generalization of the Extended Bayesian Information Criterion-Robust (EBIC-R) and it takes into account both the block structure and the high-dimensionality scenario. The analytical steps for deriving the EBIC-R for this setting are provided. Simulation results show that the proposed method performs considerably better than the existing state-of-the-art methods and achieves empirical consistency at large sample sizes and/or at high-SNR.

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“…To account for the group-sparse structure, we have relaxed the orginal covariance fitting criterion used in [19] by following the lines of [22] and thus seek to minimize…”

Section: Group-sparse Estimation Via the Covariance Fitting Criterionmentioning

confidence: 99%

“…Following the derivations in [22], minimizing (8) with respect to p and σ is equivalent of minimizing…”

Section: Group-sparse Estimation Via the Covariance Fitting Criterionmentioning

confidence: 99%

“…In fact, SPICE may shown to be equivalent to the square root (SR) LASSO [20]; in a covariance fitting sense, SPICE may be as a result be viewed as the optimal selection of the SR LASSO hyperparameter [21]. In this paper, we extend the method proposed in [22], which generalizes SPICE for grouped variables, along the lines of [23] to form recursive estimates in an online-fashion, reminiscent to the approach used in [24]. By first reformulating group-SPICE as an SR-LASSO, we then derive an efficient method for sparse recursive estimation formed via proximal gradient iterations, enabling recursive estimation of nonstationary signals.…”

Section: Introductionmentioning

confidence: 99%

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Online group-sparse estimation using the covariance fitting criterion

Kronvall

Adalbjörnsson

Nadig

et al. 2017

2017 25th European Signal Processing Conference (EUSIPCO)

Self Cite

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In this paper, we present a time-recursive implementation of a recent hyperparameter-free group-sparse estimation technique. This is achieved by reformulating the original method, termed group-SPICE, as a square-root group-LASSO with a suitable regularization level, for which a time-recursive implementation is derived. Using a proximal gradient step for lowering the computational cost, the proposed method may effectively cope with data sequences consisting of both stationary and non-stationary signals, such as transients, and/or amplitude modulated signals. Numerical examples illustrates the efficacy of the proposed method for both coherent Gaussian dictionaries and for the multi-pitch estimation problem.

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Group-sparse regression using the covariance fitting criterion

Cited by 19 publications

References 46 publications

Variational Inference of Structured Line Spectra Exploiting Group-Sparsity

Variational Inference of Structured Line Spectra Exploiting Group-Sparsity

Model Selection in High-Dimensional Block-Sparse Linear Regression

Online group-sparse estimation using the covariance fitting criterion

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