Density Sketches for Sampling and Estimation

Aditya Desai, Benjamin Coleman, Anshumali Shrivastava

Keywords: density estimation, sampling, machine learning

TL;DR: online summary of data for density estimation and sampling new data.

Abstract: There has been an exponential increase in the data generated worldwide. Insights into this data led by machine learning (ML) have given rise to exciting applications such as recommendation engines, conversational agents, and so on. Often, data for these applications is generated at a rate faster than ML pipelines can consume it. In this paper, we propose Density Sketches(DS) - a cheap and practical approach to reducing data redundancy in a streaming fashion. DS creates a succinct online summary of data distribution. While DS does not store the samples from the stream, we can sample unseen data on the fly from DS to use for downstream learning tasks. In this sense, DS can replace actual data in many machine learning pipelines analogous to generative models. Importantly, unlike generative models, which do not have statistical guarantees, the sampling distribution of DS asymptotically converges to underlying unknown density distribution.

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