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This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. Numerous renowned algorithms for tackling the compressed sensing problem…

Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…

Tensors, especially higher-order tensors, are typically represented in low-rank formats to preserve the main information of the high-dimensional data while saving memory space. In practice, only a small fraction elements in high-dimensional…

A significant hurdle for analyzing large sample data is the lack of effective statistical computing and inference methods. An emerging powerful approach for analyzing large sample data is subsampling, by which one takes a random subsample…

We present a new algorithm for finding a near optimal low-rank approximation of a matrix $A$ in $O(nnz(A))$ time. Our method is based on a recursive sampling scheme for computing a representative subset of $A$'s columns, which is then used…

Subsampling methods have been recently proposed to speed up least squares estimation in large scale settings. However, these algorithms are typically not robust to outliers or corruptions in the observed covariates. The concept of influence…

We present Automatic Laplace Collapsed Sampling (ALCS), a general framework for marginalising latent parameters in Bayesian models using automatic differentiation, which we combine with nested sampling to explore the hyperparameter space in…

Certain classes of CUR algorithms, also referred to as cross or pseudoskeleton algorithms, are widely used for low-rank matrix approximation when direct access to all matrix entries is costly. Their key advantage lies in constructing a…

Alternating minimization represents a widely applicable and empirically successful approach for finding low-rank matrices that best fit the given data. For example, for the problem of low-rank matrix completion, this method is believed to…

This paper introduces an algorithm for the nonnegative matrix factorization-and-completion problem, which aims to find nonnegative low-rank matrices X and Y so that the product XY approximates a nonnegative data matrix M whose elements are…

Low Rank Approximation is among most fundamental subjects of numerical linear algebra having important applications to various areas of modern computing and %they range from machine learning theory and %neural networks to data mining and…

Distributed adaptive signal processing has attracted much attention in the recent decade owing to its effectiveness in many decentralized real-time applications in networked systems. Because many natural signals are highly sparse with most…

This paper presents a novel adaptive reduced-rank {multi-input multi-output} (MIMO) equalization scheme and algorithms based on alternating optimization design techniques for MIMO spatial multiplexing systems. The proposed reduced-rank…

This paper proposes a new deterministic sampling strategy for constructing polynomial chaos approximations for expensive physics simulation models. The proposed approach, effectively subsampled quadratures involves sparsely subsampling an…

This paper studies the subspace segmentation problem. Given a set of data points drawn from a union of subspaces, the goal is to partition them into their underlying subspaces they were drawn from. The spectral clustering method is used as…

Low-rank plus diagonal (LRPD) decompositions provide a powerful structural model for large covariance matrices, simultaneously capturing global shared factors and localized corrections that arise in covariance estimation, factor analysis,…

Low-rank tensor sensing is a fundamental problem with broad applications in signal processing and machine learning. Among various tensor models, low-Tucker-rank tensors are particularly attractive for capturing multi-mode subspace…

A least squares semi-supervised local clustering algorithm based on the idea of compressed sensing is proposed to extract clusters from a graph with known adjacency matrix. The algorithm is based on a two-stage approach similar to the one…

Supervised machine learning and deep learning require a large amount of labeled data, which data scientists obtain in a manual, and time-consuming annotation process. To mitigate this challenge, Active Learning (AL) proposes promising data…

In this paper, we describe a new algorithm to build a few sparse principal components from a given data matrix. Our approach does not explicitly create the covariance matrix of the data and can be viewed as an extension of the Kogbetliantz…