Privately Counting Partially Ordered Data
Matthew Joseph, M\'onica Ribero, Alexander Yu
TL;DR
This paper introduces a new differentially private counting mechanism tailored for data with partial order structures, significantly reducing error compared to existing methods.
Contribution
The paper presents a novel $K$-norm mechanism for differentially private counting on partially ordered data, with efficient $O(d^2)$ runtime and superior accuracy.
Findings
Our mechanism outperforms existing private counting methods in various partial order scenarios.
Experiments demonstrate error reduction by an order of magnitude or more.
The $K$-norm approach is problem-specific and computationally efficient.
Abstract
We consider differentially private counting when each data point consists of bits satisfying a partial order. Our main technical contribution is a problem-specific -norm mechanism that runs in time . Experiments show that, depending on the partial order in question, our solution dominates existing pure differentially private mechanisms, and can reduce their error by an order of magnitude or more.
Peer Reviews
Decision·ICLR 2025 Poster
1. Summing over items with partial orders is a fundamental problem that has not been fully studied under differential privacy. 2. The proposed algorithm is very time-efficient, only quadratic in the number of bits. The speed-up is significant over some simple sampling algorithms 3. The estimation error is much better than standard privacy algorithms based on $\ell_{\infty}$ norm.
1. The algorithm is only for pure differential privacy. Approximate DP is sometimes more practical in many applications. 2. It would be helpful to the readers to provide a high-level overview of the algorithm and why it improves over standard algorithms through a simple example.
The paper proposes a sampling mechanism for a special instantiation of K-norm mechanism that improves the state of the art sampling algorithm by a factor of $O(d^\omega)$.
I found the paper rather hard to read and also difficult to figure out what are the contributions of the authors and what follows more or less from Chappell et al. (2017). I suggest that the authors make it explicitly clear by giving a high level overview of their proof stating clearly what steps requires their proof and what was already known in the literature. To me, it feels like the main contribution is the proof of Lemma 3.14, but I can be wrong and would love to stand corrected. If the a
- Brings in tools from another research area to improve algorithms/bounds for a natural and practical problem
- The paper is difficult to read for someone who is not an expert in partial orders.
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Taxonomy
TopicsPrivacy-Preserving Technologies in Data · Data Quality and Management · Cryptography and Data Security