Related papers: Sparse Approximate Solutions to Max-Plus Equations…
The subspace approximation problem Subspace($k$,$p$) asks for a $k$-dimensional linear subspace that fits a given set of points optimally, where the error for fitting is a generalization of the least squares fit and uses the $\ell_{p}$ norm…
We consider the problem of multivariate regression in a setting where the relevant predictors could be shared among different responses. We propose an algorithm which decomposes the coefficient matrix into the product of a long matrix and a…
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…
We study adaptive approximation algorithms for general multivariate linear problems where the sets of input functions are non-convex cones. While it is known that adaptive algorithms perform essentially no better than non-adaptive…
Flexible sparsity regularization means stably approximating sparse solutions of operator equations by using coefficient-dependent penalizations. We propose and analyse a general nonconvex approach in this respect, from both theoretical and…
This paper considers the stochastic convex composite optimization problem and presents multi-cut stochastic approximation (SA) methods for solving it, whose models in expectation overestimate its objective function. The multi-cut model…
In this paper, we propose three methods to solve the PageRank problem for the transition matrices with both row and column sparsity. Our methods reduce the PageRank problem to the convex optimization problem over the simplex. The first…
We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe…
We develop a new approximative estimation method for conditional Shapley values obtained using a linear regression model. We develop a new estimation method and outperform existing methodology and implementations. Compared to the sequential…
In an effort to develop an alternative approach to traditional sparse reformulations, we will provide a new type of convex reformulation of a large class of stochastic quadratically constrained quadratic optimization problems that is…
We consider the problem of \textit{online sparse linear approximation}, where one predicts the best sparse approximation of a sequence of measurements in terms of linear combination of columns of a given measurement matrix. Such online…
In this paper we present a first-order method that admits near-optimal convergence rates for convex/concave min-max problems while requiring a simple and intuitive analysis. Similarly to the seminal work of Nemirovski and the recent…
We consider the sparse optimization problem with nonlinear constraints and an objective function, which is given by the sum of a general smooth mapping and an additional term defined by the $ \ell_0 $-quasi-norm. This term is used to obtain…
An approach to obtaining a parsimonious polynomial model from time series is proposed. An optimal minimal nonuniform time series embedding schema is used to obtain a time delay kernel. This scheme recursively optimizes an objective…
We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…
The randomized version of the Kaczmarz method for the solution of linear systems is known to converge linearly in expectation. In this work we extend this result and show that the recently proposed Randomized Sparse Kaczmarz method for…
In recent years, the use of sparse recovery techniques in the approximation of high-dimensional functions has garnered increasing interest. In this work we present a survey of recent progress in this emerging topic. Our main focus is on the…
We propose a novel approximation hierarchy for cardinality-constrained, convex quadratic programs that exploits the rank-dominating eigenvectors of the quadratic matrix. Each level of approximation admits a min-max characterization whose…
Instance sparsification is well-known in the world of exact computation since it is very closely linked to the Exponential Time Hypothesis. In this paper, we extend the concept of sparsification in order to capture subexponential time…
Motivated by recent work on stochastic gradient descent methods, we develop two stochastic variants of greedy algorithms for possibly non-convex optimization problems with sparsity constraints. We prove linear convergence in expectation to…