MIT Libraries homeMIT Libraries logoDSpace@MIT

MIT
View Item 
  • DSpace@MIT Home
  • MIT Open Access Articles
  • MIT Open Access Articles
  • View Item
  • DSpace@MIT Home
  • MIT Open Access Articles
  • MIT Open Access Articles
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Robust Estimators in High-Dimensions Without the Computational Intractability

Author(s)
Diakonikolas, Ilias; Kamath, Gautam; Kane, Daniel; Li, Jerry; Moitra, Ankur; Stewart, Alistair; ... Show more Show less
Thumbnail
DownloadPublished version (1004.Kb)
Terms of use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Metadata
Show full item record
Abstract
We study high-dimensional distribution learning in an agnostic setting where an adversary is allowed to arbitrarily corrupt an ϵ-fraction of the samples. Such questions have a rich history spanning statistics, machine learning, and theoretical computer science. Even in the most basic settings, the only known approaches are either computat ionally inefficient or lose dimensiondependent factors in their error guarantees. This raises the following question: Is high-dimensional agnostic distribution learning even possible, algorithmically? In this work, we obtain the first computationally efficient algorithms with dimension-independent error guarantees for agnostically learning several fundamental classes of high-dimensional distributions: (1) a single Gaussian, (2) a product distribution on the hypercube, (3) mixtures of two product distributions (under a natural balancedness condition), and (4) mixtures of spherical Gaussians. Our a lgorithms achieve error that is independent of the dimension, and in many cases scales nearly linearly with the fraction of adversarially corrupted samples. Moreover, we develop a general recipe for detecting and correcting corruptions in high-dimensions that may be applicable to many other problems. ©2019 Society for Industrial and Applied Mathematics.
Description
from Special Section of the SIAM Journal on Computing. "Special Section on the Fifty-Seventh Annual IEEE Symposium on Foundations of Computer Science (FOCS 2016)"
Date issued
2019-04
URI
https://hdl.handle.net/1721.1/126386
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
SIAM Journal on Computing
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Citation
Diakonikolas, Ilias et al., "Robust Estimators in High-Dimensions Without the Computational Intractability." SIAM Journal on Computing 48, 2 (April 2019): p. 742–864 doi. 10.1137/17M1126680 ©2019 Authors
Version: Final published version
ISSN
1095-7111

Collections
  • MIT Open Access Articles

Browse

All of DSpaceCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

My Account

Login

Statistics

OA StatisticsStatistics by CountryStatistics by Department
MIT Libraries homeMIT Libraries logo

Find us on

Twitter Facebook Instagram YouTube RSS

MIT Libraries navigation

SearchHours & locationsBorrow & requestResearch supportAbout us
PrivacyPermissionsAccessibility
MIT
Massachusetts Institute of Technology
Content created by the MIT Libraries, CC BY-NC unless otherwise noted. Notify us about copyright concerns.