Work

Data Structures for Density Estimation

Year: 2023

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2306.11312

Authors: Aamand, Anders, Andoni, Alexandr, Chen, Justin Y., Indyk, Piotr, Narayanan, Shyam, Silwal, Sandeep

Institutions: MIT Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Columbia University

Language: English

Topic: Complexity and Algorithms in Graphs

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Office of Naval Research

Awards: Collaborative Research: AF: Small: Fine-Grained Complexity of Approximate Problems, G4720003262, AF:Small: Data-Dependent Algorithms for High-Dimensional Data, Graduate Research Fellowship Program (GRFP), Foundations of Data Science Institute, G8876996369

OpenAlex ID: W4381573445

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