Locality Sensitive Filters are known for offering a quasi-linear space data structure with rigorous guarantees for the Approximate Near Neighbor search problem. Building on Locality Sensitive Filters, we derive a simple data structure for the Approximate Near Neighbor Counting problem under differential privacy. Moreover, we provide a simple analysis leveraging a connection with concomitant statistics and extreme value theory. Our approach achieves the same performance as the recent findings of Andoni et al. (NeurIPS 2023) but with a more straightforward method. As a side result, the paper provides a more compact description and analysis of Locality Sensitive Filters for Approximate Near Neighbor Search under inner product similarity, improving a previous result in Aum\"{u}ller et al. (TODS 2022).

翻译：局部敏感滤波器因其为近似近邻搜索问题提供具有严格保证的拟线性空间数据结构而闻名。基于局部敏感滤波器，我们推导出一种适用于差分隐私下近似近邻计数问题的简单数据结构。此外，我们通过结合伴随统计量与极值理论的关联性提供了简洁的分析。该方法实现了与Andoni等人（NeurIPS 2023）近期研究相同的性能，但采用了更直接的技术路径。作为附带成果，本文针对内积相似度下的近似近邻搜索问题，给出了局部敏感滤波器更紧凑的描述与分析，改进了Aumüller等人（TODS 2022）的先前结果。