## Abstract

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/ε^{2}) log n + O(2^{k}/ε^{2}) subcube conditioning queries, and • An algorithm for testing k-junta distributions with Õ((k + √n)/ε^{2}) 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 language | English |
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Pages (from-to) | 1060-1113 |

Number of pages | 54 |

Journal | Proceedings of Machine Learning Research |

Volume | 134 |

State | Published - 2021 |

Externally published | Yes |

Event | 34th Conference on Learning Theory, COLT 2021 - Boulder, United States Duration: 15 Aug 2021 → 19 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