The Sample Complexity of Distribution-Free Parity Learning in the Robust Shuffle Model

• URL: http://arxiv.org/abs/2103.15690v1
• Date: Mon, 29 Mar 2021 15:26:02 GMT
• Title: The Sample Complexity of Distribution-Free Parity Learning in the Robust Shuffle Model
• Authors: Kobbi Nissim and Chao Yan
• Abstract summary: We show that the sample complexity of learning $d$-bit parity functions is $Omega (2d/2)$. We also sketch a simple shuffle model protocol demonstrating that our results are tight up to $poly(d)$ factors.
• Score: 11.821892196198457
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We provide a lowerbound on the sample complexity of distribution-free parity learning in the realizable case in the shuffle model of differential privacy. Namely, we show that the sample complexity of learning $d$-bit parity functions is $\Omega(2^{d/2})$. Our result extends a recent similar lowerbound on the sample complexity of private agnostic learning of parity functions in the shuffle model by Cheu and Ullman. We also sketch a simple shuffle model protocol demonstrating that our results are tight up to $poly(d)$ factors.

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