TY - GEN

T1 - Robust Estimation of Sparse Signal with Unknown Sparsity Cluster Value

AU - Belitser, Eduard

AU - Nurushev, Nurzhan

AU - Serra, Paulo

PY - 2020

Y1 - 2020

N2 - In the signal+noise model, we assume that the signal has a more general sparsity structure in the sense that the majority of signal coordinates are equal to some value which is assumed to be unknown, contrary to the classical sparsity context where one knows the sparsity cluster value (typically, zero by default). We apply an empirical Bayes approach (linked to the penalization method) for inference on the signal, possibly sparse in this more general sense. The resulting method is robust in that we do not need to know the sparsity cluster value; in fact, the method extracts as much generalized sparsity as there is in the underlying signal. However, as compared to the case of known sparsity cluster value, the proposed robust method cannot be reduced to thresholding procedure anymore. We propose two new procedures: the empirical Bayes model averaging (EBMA) and empirical Bayes model selection (EBMS) procedures, respectively. The former is procedure realized by an MCMC algorithm based on the partial (mixed) normal–normal conjugacy build in our modeling stage, and the latter is based on a new optimization algorithm of complexity. We perform simulations to demonstrate how the proposed procedures work and accommodate possible systematic error in the sparsity cluster value.

AB - In the signal+noise model, we assume that the signal has a more general sparsity structure in the sense that the majority of signal coordinates are equal to some value which is assumed to be unknown, contrary to the classical sparsity context where one knows the sparsity cluster value (typically, zero by default). We apply an empirical Bayes approach (linked to the penalization method) for inference on the signal, possibly sparse in this more general sense. The resulting method is robust in that we do not need to know the sparsity cluster value; in fact, the method extracts as much generalized sparsity as there is in the underlying signal. However, as compared to the case of known sparsity cluster value, the proposed robust method cannot be reduced to thresholding procedure anymore. We propose two new procedures: the empirical Bayes model averaging (EBMA) and empirical Bayes model selection (EBMS) procedures, respectively. The former is procedure realized by an MCMC algorithm based on the partial (mixed) normal–normal conjugacy build in our modeling stage, and the latter is based on a new optimization algorithm of complexity. We perform simulations to demonstrate how the proposed procedures work and accommodate possible systematic error in the sparsity cluster value.

KW - Empirical Bayes

KW - Sparce signal

KW - Unknow sparsity cluster value

UR - http://www.scopus.com/inward/record.url?scp=85097285371&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85097285371&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-57306-5_8

DO - 10.1007/978-3-030-57306-5_8

M3 - Conference contribution

AN - SCOPUS:85097285371

SN - 9783030573058

T3 - Springer Proceedings in Mathematics and Statistics

SP - 77

EP - 87

BT - Nonparametric Statistics

A2 - La Rocca, Michele

A2 - Liseo, Brunero

A2 - Salmaso, Luigi

PB - Springer

T2 - 4th Conference of the International Society for Nonparametric Statistics, ISNPS 2018

Y2 - 11 June 2018 through 15 June 2018

ER -