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arXiv · 2306.11312

Data Structures for Density Estimation

Anders Aamand·Alexandr Andoni·Justin Y. Chen·Piotr Indyk·Shyam Narayanan·Sandeep Silwal
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Abstract

We study statistical/computational tradeoffs for the following density estimation problem: given $k$ distributions $v_1, \ldots, v_k$ over a discrete domain of size $n$, and sampling access to a distribution $p$, identify $v_i$ that is "close" to $p$. Our main result is the first data structure that, given a sublinear (in $n$) number of samples from $p$, identifies $v_i$ in time sublinear in $k$. We also give an improved version of the algorithm of Acharya et al. (2018) that reports $v_i$ in time linear in $k$. The experimental evaluation of the latter algorithm shows that it achieves a significant reduction in the number of operations needed to achieve a given accuracy compared to prior work.

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Anders Aamand, Alexandr Andoni, Justin Y. Chen, Piotr Indyk, Shyam Narayanan, Sandeep Silwal. 2023-06-20. Data Structures for Density Estimation. https://arxiv.org/abs/2306.11312

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