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Momentum Iterative Hessian Sketch (M-IHS) techniques, a group of solvers for large scale regularized linear Least Squares (LS) problems, are proposed and analyzed in detail. Proposed M-IHS techniques are obtained by incorporating the Heavy…

Selecting a good column (or row) subset of massive data matrices has found many applications in data analysis and machine learning. We propose a new adaptive sampling algorithm that can be used to improve any relative-error column selection…

In this paper, we derive a randomized version of the Mirror-Prox method for solving some structured matrix saddle-point problems, such as the maximal eigenvalue minimization problem. Deterministic first-order schemes, such as Nesterov's…

The Hadamard decomposition is a powerful technique for data analysis and matrix compression, which decomposes a given matrix into the element-wise product of two or more low-rank matrices. In this paper, we develop an efficient algorithm to…

Standard numerical algorithms like the fast multipole method or $\mathcal{H}$-matrix schemes rely on low-rank approximations of the underlying kernel function. For high-frequency problems, the ranks grow rapidly as the mesh is refined, and…

Hierarchical matrices provide a highly memory-efficient way of storing dense linear operators arising, for example, from boundary element methods, particularly when stored in the H^2 format. In such data-sparse representations, iterative…

We develop hierarchically quantized efficient embedding representations for similarity-based search and show that this representation provides not only the state of the art performance on the search accuracy but also provides several orders…

We present an iterative method for the search of extreme entries in low-rank tensors which is based on a power iteration combined with a binary search. In this work we use the HT-format for low-rank tensors but other low-rank formats can be…

Probabilistic ideas and tools have recently begun to permeate into several fields where they had traditionally not played a major role, including fields such as numerical linear algebra and optimization. One of the key ways in which these…

This survey highlights the recent advances in algorithms for numerical linear algebra that have come from the technique of linear sketching, whereby given a matrix, one first compresses it to a much smaller matrix by multiplying it by a…

Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the…

Recent advances in the field of machine learning open a new era in high performance computing. Applications of machine learning algorithms for the development of accurate and cost-efficient surrogates of complex problems have already…

Matrix completion, i.e., the exact and provable recovery of a low-rank matrix from a small subset of its elements, is currently only known to be possible if the matrix satisfies a restrictive structural constraint---known as {\em…

Rank deficient Hankel matrices are at the core of several applications. However, in practice, the coefficients of these matrices are noisy due to e.g. measurements errors and computational errors, so generically the involved matrices are…

In this paper, we propose a low rank approximation method for efficiently solving stochastic partial differential equations. Specifically, our method utilizes a novel low rank approximation of the stiffness matrices, which can significantly…

For a linear complementarity problem, we present a relaxaiton accelerated two-sweep matrix splitting iteration method. The convergence analysis illustrates that the proposed method converges to the exact solution of the linear…

The problem of finding the missing values of a matrix given a few of its entries, called matrix completion, has gathered a lot of attention in the recent years. Although the problem under the standard low rank assumption is NP-hard,…

We present HARP, a novel method for learning low dimensional embeddings of a graph's nodes which preserves higher-order structural features. Our proposed method achieves this by compressing the input graph prior to embedding it, effectively…

In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form…

Hypergraphs serve as an effective tool widely adopted to characterize higher-order interactions in complex systems. The most intuitive and commonly used mathematical instrument for representing a hypergraph is the incidence matrix, in which…