Related papers: A Fast Greedy Algorithm for Generalized Column Sub…
We study sparse approximate solutions to convex optimization problems. It is known that in many engineering applications researchers are interested in an approximate solution of an optimization problem as a linear combination of elements…
Structured data in the form of tabular datasets contain features that are distinct and discrete, with varying individual and relative importances to the target. Combinations of one or more features may be more predictive and meaningful than…
In many machine learning applications, one needs to interactively select a sequence of items (e.g., recommending movies based on a user's feedback) or make sequential decisions in a certain order (e.g., guiding an agent through a series of…
A novel and detailed convergence analysis is presented for a greedy algorithm that was previously introduced for operator reconstruction problems in the field of quantum mechanics. This algorithm is based on an offline/online decomposition…
The Restricted Invertibility problem is the problem of selecting the largest subset of columns of a given matrix $X$, while keeping the smallest singular value of the extracted submatrix above a certain threshold. In this paper, we address…
Consider a collection of weighted subsets of a ground set N. Given a query subset Q of N, how fast can one (1) find the weighted sum over all subsets of Q, and (2) sample a subset of Q proportionally to the weights? We present a tree-based…
In this paper, we consider a novel two-dimensional randomized Kaczmarz method and its improved version with simple random sampling, which chooses two active rows with probability proportional to the square of their cross-product-like…
We describe a parallel approximation algorithm for maximizing monotone submodular functions subject to hereditary constraints on distributed memory multiprocessors. Our work is motivated by the need to solve submodular optimization problems…
Consider the Hitting Set problem where, for a given universe $\mathcal{X} = \left\{ 1, ... , n \right\}$ and a collection of subsets $\mathcal{S}_1, ... , \mathcal{S}_m$, one seeks to identify the smallest subset of $\mathcal{X}$ which has…
For many popular graph metric sparsifiers, such as spanners, emulators, and preservers, simple and elegant greedy algorithms are known that achieve state-of-the-art or existentially optimal tradeoffs between size and quality. The goal of…
Modern datasets span billions of samples, making training on all available data infeasible. Selecting a high quality subset helps in reducing training costs and enhancing model quality. Submodularity, a discrete analogue of convexity, is…
This paper examines the problem of locating outlier columns in a large, otherwise low-rank, matrix. We propose a simple two-step adaptive sensing and inference approach and establish theoretical guarantees for its performance; our results…
The coordinate descent method is an effective iterative method for solving large linear least-squares problems. In this paper, for the highly coherent columns case, we construct an effective coordinate descent method which iteratively…
In problems involving matrix computations, the concept of leverage has found a large number of applications. In particular, leverage scores, which relate the columns of a matrix to the subspaces spanned by its leading singular vectors, are…
Identifying breakpoints in piecewise regression is critical in enhancing the reliability and interpretability of data fitting. In this paper, we propose novel algorithms based on the greedy algorithm to accurately and efficiently identify…
Sparse approximation is important in many applications because of concise form of an approximant and good accuracy guarantees. The theory of compressed sensing, which proved to be very useful in the image processing and data sciences, is…
In their standard form Gaussian processes (GPs) provide a powerful non-parametric framework for regression and classificaton tasks. Their one limiting property is their $\mathcal{O}(N^{3})$ scaling where $N$ is the number of training data…
We study the problem of scheduling sensors in a resource-constrained linear dynamical system, where the objective is to select a small subset of sensors from a large network to perform the state estimation task. We formulate this problem as…
Subset selection in multiple linear regression aims to choose a subset of candidate explanatory variables that tradeoff fitting error (explanatory power) and model complexity (number of variables selected). We build mathematical programming…
The Coin Change problem, also known as the Change-Making problem, is a well-studied combinatorial optimization problem, which involves minimizing the number of coins needed to make a specific change amount using a given set of coin…