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   Zhu, Yuqing (April 2022, Proceedings of Machine Learning Research)

   We provide an end-to-end Renyi DP based-framework for differentially private top-𝑘 selection. Unlike previous approaches, which require a data-independent choice on 𝑘, we propose to privately release a data-dependent choice of 𝑘 such that the gap between 𝑘-th and the (𝑘+1)st “quality” is large. This is achieved by an extension of the Report-Noisy-Max algorithm with a more concentrated Gaussian noise. Not only does this eliminates one hyperparameter, the adaptive choice of 𝑘 also certifies the stability of the top-𝑘 indices in the unordered set so we can release them using a combination of the propose-test-release (PTR) framework and the Distance-to-Stability mechanism. We show that our construction improves the privacy-utility trade-offs compared to the previous top-𝑘 selection algorithms theoretically and empirically. Additionally, we apply our algorithm to “Private Aggregation of Teacher Ensembles (PATE)” in multi-label classification tasks with a large number of labels and show that it leads to significant performance gains. 

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   Aronov, Boris; Cardinal, Jean (January 2021, Discrete & Computational Geometry)

   We prove that some exact geometric pattern matching problems reduce in linear time to 𝑘-SUM when the pattern has a fixed size 𝑘. This holds in the real RAM model for searching for a similar copy of a set of 𝑘≥3 points within a set of n points in the plane, and for searching for an affine image of a set of 𝑘≥𝑑+2 points within a set of n points in d-space. As corollaries, we obtain improved real RAM algorithms and decision trees for the two problems. In particular, they can be solved by algebraic decision trees of near-linear height. 

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