Data Structures for Density Estimation

• URL: http://arxiv.org/abs/2306.11312v1
• Date: Tue, 20 Jun 2023 06:13:56 GMT
• Title: Data Structures for Density Estimation
• Authors: Anders Aamand, Alexandr Andoni, Justin Y. Chen, Piotr Indyk, Shyam Narayanan, Sandeep Silwal
• Abstract summary: Given a sublinear (in $n$) number of samples from $p$, our main result is the first data structure that identifies $v_i$ in time sublinear in $k$. We also give an improved version of the algorithm of Acharya et al. that reports $v_i$ in time linear in $k$.
• Score: 66.36971978162461
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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