Related papers: Total Least Squares Regression in Input Sparsity T…
We provide new high-accuracy randomized algorithms for solving linear systems and regression problems that are well-conditioned except for $k$ large singular values. For solving such $d \times d$ positive definite system our algorithms…
Following the breakthrough work of Tardos in the bit-complexity model, Vavasis and Ye gave the first exact algorithm for linear programming in the real model of computation with running time depending only on the constraint matrix. For…
We study computational-statistical gaps for improper learning in sparse linear regression. More specifically, given $n$ samples from a $k$-sparse linear model in dimension $d$, we ask what is the minimum sample complexity to efficiently (in…
I present here a pedagogical introduction to the works by Rashel Tublin and Yan V. Fyodorov on random linear systems with quadratic constraints, using tools from Random Matrix Theory and replicas. These notes illustrate and complement the…
The textbook algorithm for real-weighted single-source shortest paths takes $O(mn)$ time on a graph with $m$ edges and $n$ vertices. A recent breakthrough algorithm by [Fin24] takes $\tilde{O}(mn^{8/9})$ randomized time. The running time…
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 $n$…
The problem of fitting experimental data to a given model function $f(t; p_1,p_2,\dots,p_N)$ is conventionally solved numerically by methods such as that of Levenberg-Marquardt, which are based on approximating the Chi-squared measure of…
The paper addresses the model reduction problem by least squares moment matching for continuous-time, linear, time-invariant systems. The basic idea behind least squares moment matching is to approximate a transfer function by ensuring that…
Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…
A matrix algorithm runs superfast (aka at sublinear cost) if it involves much fewer flops and memory cells than an input matrix has entries. Big Data are frequently represented by matrices of immense sizes that cannot be handled directly…
The question of fast convergence in the classical problem of high dimensional linear regression has been extensively studied. Arguably, one of the fastest procedures in practice is Iterative Hard Thresholding (IHT). Still, IHT relies…
The parametric shortest path problem is to find the shortest paths in graph where the edge costs are of the form w_ij+lambda where each w_ij is constant and lambda is a parameter that varies. The problem is to find shortest path trees for…
The aim of this paper is two-fold: firstly, to present subspace embedding properties for $s$-hashing sketching matrices, with $s\geq 1$, that are optimal in the projection dimension $m$ of the sketch, namely, $m=\mathcal{O}(d)$, where $d$…
We propose a novel algorithm for greedy forward feature selection for regularized least-squares (RLS) regression and classification, also known as the least-squares support vector machine or ridge regression. The algorithm, which we call…
One way to understand time-series data is to identify the underlying dynamical system which generates it. This task can be done by selecting an appropriate model and a set of parameters which best fits the dynamics while providing the…
In this paper we formulate and solve a robust least squares problem for a system of linear equations subject to quantization error in the data matrix. Ordinary least squares fails to consider uncertainty in the operator, modeling all noise…
We study the computational cost of recovering a unit-norm sparse principal component $x \in \mathbb{R}^n$ planted in a random matrix, in either the Wigner or Wishart spiked model (observing either $W + \lambda xx^\top$ with $W$ drawn from…
Consider an undirected weighted graph $G = (V,E,w)$. We study the problem of computing $(1+\epsilon)$-approximate shortest paths for $S \times V$, for a subset $S \subseteq V$ of $|S| = n^r$ sources, for some $0 < r \le 1$. We devise a…
We present a new algorithm and the corresponding convergence analysis for the regularization of linear inverse problems with sparsity constraints, applied to a new generalized sparsity promoting functional. The algorithm is based on the…
In the famous least sum of trimmed squares (LTS) of residuals estimator (Rousseeuw (1984)), residuals are first squared and then trimmed. In this article, we first trim residuals - using a depth trimming scheme - and then square the rest of…