Year: 2025
Type: preprint
Abstract: We study the problem of learning junta distributions on {±1}ⁿ, where a distribution is a k-junta if its probability mass function depends on a subset of at most k variables. We make two main contributions: - We show that learning k-junta distributions is computationally equivalent to learning k-parity functions with noise (LPN), a landmark problem in computational learning theory. - We design an algorithm for learning junta distributions whose statistical complexity is optimal, up to polylogarithmic factors. Computationally, our algorithm matches the complexity of previous (non-sample-optimal) algorithms. Combined, our two contributions imply that our algorithm cannot be significantly improved, statistically or computationally, barring a breakthrough for LPN.
Source: arXiv (Cornell University)
Author: Beretta, Lorenzo
Institution: University of California, Santa Cruz
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414686732
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