Related papers: Turnstile $\ell_p$ leverage score sampling with ap…
Recent works in dimensionality reduction for regression tasks have introduced the notion of sensitivity, an estimate of the importance of a specific datapoint in a dataset, offering provable guarantees on the quality of the approximation…
Recently there has been much work on selective sampling, an online active learning setting, in which algorithms work in rounds. On each round an algorithm receives an input and makes a prediction. Then, it can decide whether to query a…
A technique introduced by Indyk and Woodruff [STOC 2005] has inspired several recent advances in data-stream algorithms. We show that a number of these results follow easily from the application of a single probabilistic method called…
Given a vector $x \in \mathbb{R}^n$ induced by a turnstile stream $S$, a non-negative function $G: \mathbb{R} \to \mathbb{R}$, a perfect $G$-sampler outputs an index $i$ with probability $\frac{G(x_i)}{\sum_{j\in[n]}…
It is common to show the confidence intervals or $p$-values of selected features, or predictor variables in regression, but they often involve selection bias. The selective inference approach solves this bias by conditioning on the…
Randomized algorithms for very large matrix problems have received a great deal of attention in recent years. Much of this work was motivated by problems in large-scale data analysis, and this work was performed by individuals from many…
We give the first algorithm for kernel Nystr\"om approximation that runs in *linear time in the number of training points* and is provably accurate for all kernel matrices, without dependence on regularity or incoherence conditions. The…
While leverage score sampling provides powerful tools for approximating solutions to large least squares problems, the cost of computing exact scores and sampling often prohibits practical application. This paper addresses this challenge by…
We focus on \emph{row sampling} based approximations for matrix algorithms, in particular matrix multipication, sparse matrix reconstruction, and \math{\ell_2} regression. For \math{\matA\in\R^{m\times d}} (\math{m} points in \math{d\ll m}…
Originally introduced in game theory, Shapley values have emerged as a central tool in explainable machine learning, where they are used to attribute model predictions to specific input features. However, computing Shapley values exactly is…
We study active sampling algorithms for linear regression, which aim to query only a few entries of a target vector $b\in\mathbb R^n$ and output a near minimizer to $\min_{x\in\mathbb R^d} \|Ax-b\|$, for a design matrix $A\in\mathbb R^{n…
One approach to improving the running time of kernel-based machine learning methods is to build a small sketch of the input and use it in lieu of the full kernel matrix in the machine learning task of interest. Here, we describe a version…
We explain theoretically a curious empirical phenomenon: "Approximating a matrix by deterministically selecting a subset of its columns with the corresponding largest leverage scores results in a good low-rank matrix surrogate". To obtain…
We study the selection problem, namely that of computing the $i$th order statistic of $n$ given elements. Here we offer a data structure called \emph{selectable sloppy heap} handling a dynamic version in which upon request: (i)~a new…
In the maximum coverage problem we are given $d$ subsets from a universe $[n]$, and the goal is to output $k$ subsets such that their union covers the largest possible number of distinct items. We present the first algorithm for maximum…
For obtaining optimal first-order convergence guarantee for stochastic optimization, it is necessary to use a recurrent data sampling algorithm that samples every data point with sufficient frequency. Most commonly used data sampling…
We study algorithms for estimating the statistical leverage scores of rectangular dense or sparse matrices of arbitrary rank. Our approach is based on combining rank revealing methods with compositions of dense and sparse randomized…
In this work, we propose a new randomized algorithm for computing a low-rank approximation to a given matrix. Taking an approach different from existing literature, our method first involves a specific biased sampling, with an element being…
Tensor data represents a multidimensional array. Regression methods based on low-rank tensor decomposition leverage structural information to reduce the parameter count. Multilinear logistic regression serves as a powerful tool for the…
Selecting a good column (or row) subset of massive data matrices has found many applications in data analysis and machine learning. We propose a new adaptive sampling algorithm that can be used to improve any relative-error column selection…