Fast methods for recovering sparse parameters in linear low rank models

Abstract

In this paper, we investigate the recovery of a sparse weight vector (parameters vector) from a set of noisy linear combinations. However, only partial information about the matrix representing the linear combinations is available. Assuming a low-rank structure for the matrix, one natural solution would be to first apply a matrix completion to the data, and then to solve the resulting compressed sensing problem. In big data applications such as massive MIMO and medical data, the matrix completion step imposes a huge computational burden. Here, we propose to reduce the computational cost of the completion task by ignoring the columns corresponding to zero elements in the sparse vector. To this end, we employ a technique to initially approximate the support of the sparse vector. We further propose to unify the partial matrix completion and sparse vector recovery into an augmented four-step problem. Simulation results reveal that the augmented approach achieves the best performance, while both proposed methods outperform the natural two-step technique with substantially less computational requirements.

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

“…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 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].…”

“…Recently, 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.…”

“…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.…”

EEG Signal Dimensionality Reduction and Classification using Tensor Decomposition and Deep Convolutional Neural Networks

“…In this paper, we propose an algorithm based on low-rank decomposition of tensors to reduce the size of TF representations of EEG data. Low-rank assumption is a realistic side information for many scenarios in signal processing and communication systems [14,15,16]. Firstly, a set of super-slices, which are robust superposition of all slices, is computed.…”