Learning and Testing Junta Distributions with Subcube Conditioning

Xi Chen, Rajesh Jayaram, Amit Levi, Erik Waingarten

Research output: Contribution to journalConference articlepeer-review


We study the problems of learning and testing junta distributions on {-1, 1}n with respect to the uniform distribution, where a distribution p is a k-junta if its probability mass function p(x) depends on a subset of at most k variables. The main contribution is an algorithm for finding relevant coordinates in a k-junta distribution with subcube conditioning Bhattacharyya and Chakraborty (2018); Canonne et al. (2019). We give two applications: • An algorithm for learning k-junta distributions with Õ(k/ε2) log n + O(2k2) subcube conditioning queries, and • An algorithm for testing k-junta distributions with Õ((k + √n)/ε2) subcube conditioning queries. All our algorithms are optimal up to poly-logarithmic factors. Our results show that subcube conditioning, as a natural model for accessing high-dimensional distributions, enables significant savings in learning and testing junta distributions compared to the standard sampling model. This addresses an open question posed by Aliakbarpour et al. (2016).

Original languageEnglish
Pages (from-to)1060-1113
Number of pages54
JournalProceedings of Machine Learning Research
StatePublished - 2021
Externally publishedYes
Event34th Conference on Learning Theory, COLT 2021 - Boulder, United States
Duration: 15 Aug 202119 Aug 2021

Bibliographical note

Publisher Copyright:
© 2021 X. Chen, R. Jayaram, A. Levi & E. Waingarten.

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability


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