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The self-consistent procedure in electronic structure calculations is revisited using a highly efficient and robust algorithm for solving the non-linear eigenvector problem i.e. H({{\psi}}){\psi} = E{\psi}. This new scheme is derived from a…

The problem of estimating sparse eigenvectors of a symmetric matrix attracts a lot of attention in many applications, especially those with high dimensional data set. While classical eigenvectors can be obtained as the solution of a…

This paper presents a new algorithmic framework for computing sparse solutions to large-scale linear discrete ill-posed problems. The approach is motivated by recent perspectives on iteratively reweighted norm schemes, viewed through the…

Several problems in machine learning, statistics, and other fields rely on computing eigenvectors. For large scale problems, the computation of these eigenvectors is typically performed via iterative schemes such as subspace iteration or…

Rational filter functions can be used to improve convergence of contour-based eigensolvers, a popular family of algorithms for the solution of the interior eigenvalue problem. We present a framework for the optimization of rational filters…

We consider solving the $\ell_1$-regularized least-squares ($\ell_1$-LS) problem in the context of sparse recovery, for applications such as compressed sensing. The standard proximal gradient method, also known as iterative…

Training Convolutional Neural Networks (CNNs) for very high resolution images requires a large quantity of high-quality pixel-level annotations, which is extremely labor- and time-consuming to produce. Moreover, professional photo…

Many problems in machine learning can be solved by rounding the solution of an appropriate linear program (LP). This paper shows that we can recover solutions of comparable quality by rounding an approximate LP solution instead of the ex-…

Entity Resolution suffers from quadratic time complexity. To increase its time efficiency, three kinds of filtering techniques are typically used for restricting its search space: (i) blocking workflows, which group together entity profiles…

Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…

Low-rank tensor completion problem aims to recover a tensor from limited observations, which has many real-world applications. Due to the easy optimization, the convex overlapping nuclear norm has been popularly used for tensor completion.…

It has recently been shown that ISTA, an unaccelerated optimization method, presents sparse updates for the $\ell_1$-regularized personalized PageRank problem, leading to cheap iteration complexity and providing the same guarantees as the…

The Kaczmarz method is an iterative method for solving large systems of equations that projects iterates orthogonally onto the solution space of each equation. In contrast to direct methods such as Gaussian elimination or QR-factorization,…

The idea of unfolding iterative algorithms as deep neural networks has been widely applied in solving sparse coding problems, providing both solid theoretical analysis in convergence rate and superior empirical performance. However, for…

Correspondence problems are often modelled as quadratic optimization problems over permutations. Common scalable methods for approximating solutions of these NP-hard problems are the spectral relaxation for non-convex energies and the…

In recent years, contour-based eigensolvers have emerged as a standard approach for the solution of large and sparse eigenvalue problems. Building upon recent performance improvements through non-linear least square optimization of…

Clustering short text embeddings is a foundational task in natural language processing, yet remains challenging due to the need to specify the number of clusters in advance. We introduce a scalable spectral method that estimates the number…

Iterative multiscale methods for electronic structure calculations offer several advantages for large-scale problems. Here we examine a nonlinear full approximation scheme (FAS) multigrid method for solving fixed potential and…

The success of the application of machine-learning techniques to compilation tasks can be largely attributed to the recent development and advancement of program characterization, a process that numerically or structurally quantifies a…

We consider the problem of solving floating-point constraints obtained from software verification. We present UppSAT --- a new implementation of a systematic approximation refinement framework [ZWR17] as an abstract SMT solver. Provided…