Faster Differentially Private Top-$k$ Selection: A Joint Exponential Mechanism with Pruning

• URL: http://arxiv.org/abs/2411.09552v1
• Date: Thu, 14 Nov 2024 16:06:13 GMT
• Title: Faster Differentially Private Top-$k$ Selection: A Joint Exponential Mechanism with Pruning
• Authors: Hao WU, Hanwen Zhang,
• Abstract summary: We study the differentially private top-$k$ selection problem, aiming to identify a sequence of $k$ items with approximately the highest scores from $d$ items. Recent work by Gillenwater et al. (ICML '22) employs a direct sampling approach from the vast collection of $d,Theta(k)$ possible length-$k$ sequences. We present an improved algorithm with time and space complexity $O(d + k2 / epsilon cdot ln d)$, where $epsilon$ denotes the privacy
• Score: 2.2083091880368855
• License:
• Abstract: We study the differentially private top-$k$ selection problem, aiming to identify a sequence of $k$ items with approximately the highest scores from $d$ items. Recent work by Gillenwater et al. (ICML '22) employs a direct sampling approach from the vast collection of $d^{\,\Theta(k)}$ possible length-$k$ sequences, showing superior empirical accuracy compared to previous pure or approximate differentially private methods. Their algorithm has a time and space complexity of $\tilde{O}(dk)$. In this paper, we present an improved algorithm with time and space complexity $O(d + k^2 / \epsilon \cdot \ln d)$, where $\epsilon$ denotes the privacy parameter. Experimental results show that our algorithm runs orders of magnitude faster than their approach, while achieving similar empirical accuracy.

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