Learning and testing junta distributions

Maryam Aliakbarpour, Eric Blais, Ronitt Rubinfeld

Research output: Contribution to journalConference articlepeer-review

Abstract

We consider the problem of learning distributions in the presence of irrelevant features. This problem is formalized by introducing a new notion of k-junta distributions. Informally, a distribution D over the domain Xn is a k-junta distribution with respect to another distribution U over the same domain if there is a set J ⊆ [n] of size |J| ≤ k that captures the difference between D and U. We show that it is possible to learn k-junta distributions with respect to the uniform distribution over the Boolean hypercube {0, 1}n in time poly(nk, 1/ε). This result is obtained via a new Fourier-based learning algorithm inspired by the Low-Degree Algorithm of Linial, Mansour, and Nisan (1993). We also consider the problem of testing whether an unknown distribution is a k-junta distribution with respect to the uniform distribution. We give a nearly-optimal algorithm for this task. Both the analysis of the algorithm and the lower bound showing its optimality are obtained by establishing connections between the problem of testing junta distributions and testing uniformity of weighted collections of distributions.

Original languageEnglish
Pages (from-to)19-46
Number of pages28
JournalJournal of Machine Learning Research
Volume49
Issue numberJune
StatePublished - 6 Jun 2016
Event29th Conference on Learning Theory, COLT 2016 - New York, United States
Duration: 23 Jun 201626 Jun 2016

Keywords

  • Fourier analysis
  • Juntas
  • Learning distributions
  • Property testing

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