Introduction to Coresets: Accurate Coresets

10/19/2019
by   Ibrahim Jubran, et al.
0

A coreset (or core-set) of an input set is its small summation, such that solving a problem on the coreset as its input, provably yields the same result as solving the same problem on the original (full) set, for a given family of problems (models, classifiers, loss functions). Over the past decade, coreset construction algorithms have been suggested for many fundamental problems in e.g. machine/deep learning, computer vision, graphics, databases, and theoretical computer science. This introductory paper was written following requests from (usually non-expert, but also colleagues) regarding the many inconsistent coreset definitions, lack of available source code, the required deep theoretical background from different fields, and the dense papers that make it hard for beginners to apply coresets and develop new ones. The paper provides folklore, classic and simple results including step-by-step proofs and figures, for the simplest (accurate) coresets of very basic problems, such as: sum of vectors, minimum enclosing ball, SVD/ PCA and linear regression. Nevertheless, we did not find most of their constructions in the literature. Moreover, we expect that putting them together in a retrospective context would help the reader to grasp modern results that usually extend and generalize these fundamental observations. Experts might appreciate the unified notation and comparison table that links between existing results. Open source code with example scripts are provided for all the presented algorithms, to demonstrate their practical usage, and to support the readers who are more familiar with programming than math.

READ FULL TEXT

Authors

page 1

page 2

page 3

page 4

11/04/2021

Introduction to Coresets: Approximated Mean

A strong coreset for the mean queries of a set P in ℝ^d is a small weigh...
06/09/2020

Coresets for Near-Convex Functions

Coreset is usually a small weighted subset of n input points in R^d, tha...
06/09/2020

Faster PAC Learning and Smaller Coresets via Smoothed Analysis

PAC-learning usually aims to compute a small subset (ε-sample/net) from ...
09/05/2016

Volume Raycasting mit OpenCL

This German paper was written entirely at the University of Duisburg-Ess...
04/12/2013

The Recomputation Manifesto

Replication of scientific experiments is critical to the advance of scie...
06/11/2019

Fast and Accurate Least-Mean-Squares Solvers

Least-mean squares (LMS) solvers such as Linear / Ridge / Lasso-Regressi...
11/30/2015

Coresets for Kinematic Data: From Theorems to Real-Time Systems

A coreset (or core-set) of a dataset is its semantic compression with re...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.