Related papers: Sublinear Time Low-Rank Approximation of Hankel Ma…
We consider $\ell_1$-Rank-$r$ Approximation over GF(2), where for a binary $m\times n$ matrix ${\bf A}$ and a positive integer $r$, one seeks a binary matrix ${\bf B}$ of rank at most $r$, minimizing the column-sum norm $||{\bf A} -{\bf…
We consider fast algorithms for monotone submodular maximization subject to a matroid constraint. We assume that the matroid is given as input in an explicit form, and the goal is to obtain the best possible running times for important…
A spectrally sparse signal of order $r$ is a mixture of $r$ damped or undamped complex sinusoids. This paper investigates the problem of reconstructing spectrally sparse signals from a random subset of $n$ regular time domain samples, which…
Smoothed analysis is a powerful paradigm in overcoming worst-case intractability in unsupervised learning and high-dimensional data analysis. While polynomial time smoothed analysis guarantees have been obtained for worst-case intractable…
We present a new class of preconditioned iterative methods for solving linear systems of the form $Ax = b$. Our methods are based on constructing a low-rank Nystr\"om approximation to $A$ using sparse random matrix sketching. This…
Many matrices appearing in numerical methods for partial differential equations and integral equations are rank-structured, i.e., they contain submatrices that can be approximated by matrices of low rank. A relatively general class of…
We consider the classical makespan minimization scheduling problem where $n$ jobs must be scheduled on $m$ identical machines. Using weighted random sampling, we developed two sublinear time approximation schemes: one for the case where $n$…
Given a finite metric space $(X\cup Y, \mathbf{d})$ the $k$-median problem is to find a set of $k$ centers $C\subseteq Y$ that minimizes $\sum_{p\in X} \min_{c\in C} \mathbf{d}(p,c)$. In general metrics, the best polynomial time algorithm…
We investigate the use of matrix completion methods for time-series imputation. Specifically we consider low-rank completion of the block-Hankel matrix representation of a time-series. Simulation experiments are used to compare the method…
We present novel algorithmic techniques to efficiently verify the Kruskal rank of matrices that arise in sparse linear regression, tensor decomposition, and latent variable models. Our unified framework combines randomized hashing…
The minimum realization problem of hidden Markov models (HMM's) is a fundamental question of stationary discrete-time processes with a finite alphabet. It was shown in the literature that tensor decomposition methods give the hidden Markov…
We study the decomposition of a multivariate Hankel matrix H\_$\sigma$ as a sum of Hankel matrices of small rank in correlation with the decomposition of its symbol $\sigma$ as a sum of polynomial-exponential series. We present a new…
We study the problem of finding elements in the intersection of an arbitrary conic variety in $\mathbb{F}^n$ with a given linear subspace (where $\mathbb{F}$ can be the real or complex field). This problem captures a rich family of…
The inverse of the stiffness matrix of the time-harmonic Maxwell equation with perfectly conducting boundary conditions is approximated in the blockwise low-rank format of ${\mathcal H}$-matrices. We prove that root exponential convergence…
Skew polynomials are a class of non-commutative polynomials that have several applications in computer science, coding theory and cryptography. In particular, skew polynomials can be used to construct and decode evaluation codes in several…
New algorithms are presented for computing annihilating polynomials of Toeplitz, Hankel, and more generally Toeplitz+ Hankel-like matrices over a field. Our approach follows works on Coppersmith's block Wiedemann method with structured…
Hankel tensors arise from applications such as signal processing. In this paper, we make an initial study on Hankel tensors. For each Hankel tensor, we associate it with a Hankel matrix and a higher order two-dimensional symmetric tensor,…
We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it,…
We extend the concept of polynomial time approximation algorithms to apply to problems for hierarchically specified graphs, many of which are PSPACE-complete. Assuming P != PSPACE, the existence or nonexistence of such efficient…
In this paper, we study the general problem of optimizing a convex function $F(L)$ over the set of $p \times p$ matrices, subject to rank constraints on $L$. However, existing first-order methods for solving such problems either are too…