Fast Methods for Recovering Sparse Parameters in Linear Low Rank Models

Esmaeili, Ashkan; Amini, Arash; Marvasti, Farokh

doi:10.48550/arxiv.1606.08009

Cited by 2 publications

(9 citation statements)

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Section: Methodsmentioning

confidence: 99%

“…The authors in [1] introduced a new fast approach in dealing with the combined problem of matrix completion arXiv:1611.07093v3 [stat.ML] 25 Jul 2017 and sparse recovery. In [1], authors mention that precise matrix completion and data inference on large structures are based on algorithms which are computationally complex. The well-known algorithms for matrix completion in the literature are based on singular value decomposition in consecutive iterations which does not seem to be reasonable for big data scenarios as stated in [1].…”

Section: Methodsmentioning

confidence: 99%

“…In [1], authors mention that precise matrix completion and data inference on large structures are based on algorithms which are computationally complex. The well-known algorithms for matrix completion in the literature are based on singular value decomposition in consecutive iterations which does not seem to be reasonable for big data scenarios as stated in [1]. Therefore, the authors claim that it is sufficient to implement the completion algorithm for few iterations or even apply a simple (non-complex) completion method which leads to a good approximation of the support, and afterwards confine the data matrix on the approximated support.…”

Section: Methodsmentioning

confidence: 99%

“…In this paper, our aim is to compensate for the accuracy by employing the empirical covariance matrix estimation. It is worth noting that the algorithm presented in [1] and the one we are going to mention are applicable to every method in sparse linear regression with missing data. For example, two methods on this specific topic are presented in [10], [11], [12].…”

Section: Methodsmentioning

confidence: 99%

“…In fact, this could be considered as a joint problem of missing data imputation and sparse recovery of the parameters vector (supporting columns). Similar setting for matrices is investigated in [9] by Tao, et al The rest of the paper is organized as follows: In Section II, we explain our algorithm and compare it to that in [1]. In Section III, we provide the simulation results and discuss the efficacy of out method in enhancing prediction accuracy.…”

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confidence: 99%

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Using empirical covariance matrix in enhancing prediction accuracy of linear models with Missing Information

Moradipari

Shahsavari

Esmaeili

et al. 2017

2017 International Conference on Sampling Theory and Applications (SampTA)

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Abstract-Inference and Estimation in Missing Information (MI) scenarios are important topics in Statistical Learning Theory and Machine Learning (ML). In ML literature, attempts have been made to enhance prediction through precise feature selection methods. In sparse linear models, LASSO is well-known in extracting the desired support of the signal and resisting against noisy systems. When sparse models are also suffering from MI, the sparse recovery and inference of the missing models are taken into account simultaneously. In this paper, we will introduce an approach which enjoys sparse regression and covariance matrix estimation to improve matrix completion accuracy, and as a result enhancing feature selection preciseness which leads to reduction in prediction Mean Squared Error (MSE). We will compare the effect of employing covariance matrix in enhancing estimation accuracy to the case it is not used in feature selection. Simulations show the improvement in the performance as compared to the case where the covariance matrix estimation is not used. I. INTORDUCTIONRecently, inference and learning in problems which are suffering from incomplete datasets have gained specific attention since these types of problems are accompanied with important applications in practical settings. In [1], practical settings are introduced where dealing with missing information and developing a statistical model which could learn the incomplete data are necessary. It is intuitively comprehensible that learning procedures would differ in missing data scenarios. We illustrate a novel example which could clarify what dealing with missing data means. Consider an image has missing information or lossy segments, and as a result, many pixels are lost or corrupted. In this setting, knowing the fact that the image is low-rank (few colors are used in painting for instance) helps restoration. As another illustration, suppose we have many athletes for whom specific records and measurements are gathered. The recorded features may have lots of features as not reported or not assigned (NA). Our purpose may be deriving the statistical model which Moradipari, Shahsavari, and determines the weight of each feature affecting a specific criterion such as athlete's stamina. Thus, we have a learning problem in a missing information scenario. Many works in the literature have been carried out towards the matrix completion problem including but not limited to [2], and [3]. Now, we proceed to add another aspect into the problem. In many settings, we are actually solving Compressed Sensing (CS) problems [4], where there is some sparsity pattern in the problem model. We briefly review how CS became popular in the literature. In many problems, there exists some sparsity pattern which leads to finding a unique solution for underdetermined settings provided there are sparsity constraints. CS problems have many well-known methods developed in the literature which could be classified in three main classes. One class is related to the soft-thresholding methods. ...

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

mentioning

confidence: 99%

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Using empirical covariance matrix in enhancing prediction accuracy of linear models with Missing Information

Moradipari

Shahsavari

Esmaeili

et al. 2017

2017 International Conference on Sampling Theory and Applications (SampTA)

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Iterative null space projection method with adaptive thresholding in sparse signal recovery

Esmaeili

Kangarshahi

Marvasti

2018

IET signal process.

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Adaptive thresholding methods have proved to yield high Signal-to-Noise Ratio (SNR) and fast convergence for sparse signal recovery. Recently, it was observed that the robustness of a class of iterative sparse recovery algorithms such as Iterative Method with Adaptive Thresholding (IMAT) outperforms the well-known LASSO algorithm in terms of reconstruction quality, convergence speed, and the sensitivity to the noise. In this paper, we introduce a new method towards sparse signal recovery from random samples (RS) of the sensing matrix or its generalized version Compressed Sensing (CS) problem. The logic of this method is based on iterative projections of the thresholded signal onto the null-space of the sensing matrix. The simulations results reveal that the proposed method has the capability of yielding noticeable output SNR values when the number of samples approaches twice the sparsity number, while other methods fail to recover the signals when approaching this number. We have also extended our algorithm to Matrix Completion (MC) scenarios and compared its efficiency to other well-known approaches for MC in the literature.

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Fast Methods for Recovering Sparse Parameters in Linear Low Rank Models

Cited by 2 publications

References 0 publications

Using empirical covariance matrix in enhancing prediction accuracy of linear models with Missing Information

Using empirical covariance matrix in enhancing prediction accuracy of linear models with Missing Information

Iterative null space projection method with adaptive thresholding in sparse signal recovery

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