Bayesian learning for robust principal component analysis

Sundin, Martin; Chatterjee, Saikat; Jansson, Magnus

doi:10.1109/eusipco.2015.7362807

Cited by 3 publications

References 16 publications

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Bayesian lower bounds for dense or sparse (Outlier) noise in the RMT framework

Ollier

Boyer

Korso

et al. 2016

2016 IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM)

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Abstract-Robust estimation is an important and timely research subject. In this paper, we investigate performance lower bounds on the mean-square-error (MSE) of any estimator for the Bayesian linear model, corrupted by a noise distributed according to an i.i.d. Student's t-distribution. This class of prior parametrized by its degree of freedom is relevant to modelize either dense or sparse (accounting for outliers) noise. Using the hierarchical Normal-Gamma representation of the Student's t-distribution, the Van Trees' Bayesian Cramér-Rao bound (BCRB) on the amplitude parameters is derived. Furthermore, the random matrix theory (RMT) framework is assumed, i.e., the number of measurements and the number of unknown parameters grow jointly to infinity with an asymptotic finite ratio. Using some powerful results from the RMT, closed-form expressions of the BCRB are derived and studied. Finally, we propose a framework to fairly compare two models corrupted by noises with different degrees of freedom for a fixed common target signal-to-noise ratio (SNR). In particular, we focus our effort on the comparison of the BCRBs associated with two models corrupted by a sparse noise promoting outliers and a dense (Gaussian) noise, respectively.Index Terms-Bayesian hierarchical linear model, Bayesian Cramér-Rao bound, sparse outlier noise, dense noise, random matrix theory

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Bayesian lower bounds for dense or sparse (Outlier) noise in the RMT framework

Ollier

Boyer

Korso

et al. 2016

2016 IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM)

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Nonparametric Bayesian Correlated Group Regression With Applications to Image Classification

Luo

Yang

Zhang

et al. 2018

IEEE Trans. Neural Netw. Learning Syst.

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Sparse Bayesian learning has emerged as a powerful tool to tackle various image classification tasks. The existing sparse Bayesian models usually use independent Gaussian distribution as the prior knowledge for the noise. However, this assumption often contradicts to the practical observations in which the noise is long tail and pixels containing noise are spatially correlated. To handle the practical noise, this paper proposes to partition the noise image into several 2-D groups and adopt the long-tail distribution, i.e., the scale mixture of the matrix Gaussian distribution, to model each group to capture the intragroup correlation of the noise. Under the nonparametric Bayesian estimation, the low-rank-induced prior and the matrix Gamma distribution prior are imposed on the covariance matrix of each group, respectively, to induce two Bayesian correlated group regression (BCGR) methods. Moreover, the proposed methods are extended to the case with unknown group structure. Our BCGR method provides an effective way to automatically fit the noise distribution and integrates the long-tail attribute and structure information of the practical noise into model. Therefore, the estimated coefficients are better for reconstructing the desired data. We apply BCGR to address image classification task and utilize the learned covariance matrices to construct a grouped Mahalanobis distance to measure the reconstruction residual of each class in the design of a classifier. Experimental results demonstrate the effectiveness of our new BCGR model.

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Sparse Bayesian Learning for Robust PCA: Algorithms and Analyses

Liu

Rao

2019

IEEE Trans. Signal Process.

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Bayesian learning for robust principal component analysis

Cited by 3 publications

References 16 publications

Bayesian lower bounds for dense or sparse (Outlier) noise in the RMT framework

Bayesian lower bounds for dense or sparse (Outlier) noise in the RMT framework

Nonparametric Bayesian Correlated Group Regression With Applications to Image Classification

Sparse Bayesian Learning for Robust PCA: Algorithms and Analyses

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