Related papers: Turnstile $\ell_p$ leverage score sampling with ap…
Adaptive sampling is a useful algorithmic tool for data summarization problems in the classical centralized setting, where the entire dataset is available to the single processor performing the computation. Adaptive sampling repeatedly…
One popular method for dealing with large-scale data sets is sampling. For example, by using the empirical statistical leverage scores as an importance sampling distribution, the method of algorithmic leveraging samples and rescales…
We give a simple algorithm to efficiently sample the rows of a matrix while preserving the p-norms of its product with vectors. Given an $n$-by-$d$ matrix $\boldsymbol{\mathit{A}}$, we find with high probability and in input sparsity time…
In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we…
Datasets with sheer volume have been generated from fields including computer vision, medical imageology, and astronomy whose large-scale and high-dimensional properties hamper the implementation of classical statistical models. To tackle…
We present a new algorithm for finding a near optimal low-rank approximation of a matrix $A$ in $O(nnz(A))$ time. Our method is based on a recursive sampling scheme for computing a representative subset of $A$'s columns, which is then used…
We focus the use of \emph{row sampling} for approximating matrix algorithms. We give applications to matrix multipication; sparse matrix reconstruction; and, \math{\ell_2} regression. For a matrix \math{\matA\in\R^{m\times d}} which…
Random sampling has become a critical tool in solving massive matrix problems. For linear regression, a small, manageable set of data rows can be randomly selected to approximate a tall, skinny data matrix, improving processing time…
Leverage score sampling provides an appealing way to perform approximate computations for large matrices. Indeed, it allows to derive faithful approximations with a complexity adapted to the problem at hand. Yet, performing leverage scores…
We present the first feasible method for sampling a dynamic data stream with deletions, where the sample consists of pairs $(k,C_k)$ of a value $k$ and its exact total count $C_k$. Our algorithms are for both Strict Turnstile data streams…
In large scale machine learning, random sampling is a popular way to approximate datasets by a small representative subset of examples. In particular, sensitivity sampling is an intensely studied technique which provides provable guarantees…
Ridge leverage scores provide a balance between low-rank approximation and regularization, and are ubiquitous in randomized linear algebra and machine learning. Deterministic algorithms are also of interest in the moderately big data…
The seminal work of Cohen and Peng introduced Lewis weight sampling to the theoretical computer science community, yielding fast row sampling algorithms for approximating $d$-dimensional subspaces of $\ell_p$ up to $(1+\epsilon)$ error.…
We study the $\ell_p$ regression problem, which requires finding $\mathbf{x}\in\mathbb R^{d}$ that minimizes $\|\mathbf{A}\mathbf{x}-\mathbf{b}\|_p$ for a matrix $\mathbf{A}\in\mathbb R^{n \times d}$ and response vector…
For massive data, the family of subsampling algorithms is popular to downsize the data volume and reduce computational burden. Existing studies focus on approximating the ordinary least squares estimate in linear regression, where…
The statistical leverage scores of a matrix $A$ are the squared row-norms of the matrix containing its (top) left singular vectors and the coherence is the largest leverage score. These quantities are of interest in recently-popular…
Random features provide a practical framework for large-scale kernel approximation and supervised learning. It has been shown that data-dependent sampling of random features using leverage scores can significantly reduce the number of…
Suppose an $n \times d$ design matrix in a linear regression problem is given, but the response for each point is hidden unless explicitly requested. The goal is to sample only a small number $k \ll n$ of the responses, and then produce a…
The demand of computational resources for the modeling process increases as the scale of the datasets does, since traditional approaches for regression involve inverting huge data matrices. The main problem relies on the large data size,…
There has been significant interest and progress recently in algorithms that solve regression problems involving tall and thin matrices in input sparsity time. These algorithms find shorter equivalent of a n*d matrix where n >> d, which…