Learning and smoothed analysis

Adam Tauman Kalai, Alex Samorodnitsky, Shang Hua Teng

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

34 Scopus citations

Abstract

We give a new model of learning motivated by smoothed analysis (Spielman and Teng, 2001). In this model, we analyze two new algorithms, for PAC-learning DNFs and agnostically learning decision trees, from random examples drawn from a constant-bounded product distributions. These two problems had previously been solved using membership queries (Jackson, 1995; Gopalan et al, 2005). Our analysis demonstrates that the "heavy" Fourier coefficients of a DNF suffice to recover the DNF. We also show that a structural property of the Fourier spectrum of any boolean function over "typical" product distributions. In a second model, we consider a simple new distribution over the boolean hypercube, one which is symmetric but is not the uniform distribution, from which we can learn O(log n)-depth decision trees in polynomial time.

Original languageAmerican English
Title of host publicationProceedings - 50th Annual Symposium on Foundations of Computer Science, FOCS 2009
Pages395-404
Number of pages10
DOIs
StatePublished - 2009
Event50th Annual Symposium on Foundations of Computer Science, FOCS 2009 - Atlanta, GA, United States
Duration: 25 Oct 200927 Oct 2009

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
ISSN (Print)0272-5428

Conference

Conference50th Annual Symposium on Foundations of Computer Science, FOCS 2009
Country/TerritoryUnited States
CityAtlanta, GA
Period25/10/0927/10/09

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