A smoothed-Bayesian approach to frequency recovery from sketched data

TL;DR

This paper introduces a smoothed-Bayesian method for accurately recovering symbol frequencies from compressed sketch data, offering computational efficiency and strong theoretical guarantees, especially for large-scale and complex distributions.

Contribution

It presents a novel frequentist framework for Bayesian-inspired frequency estimation from sketches, addressing computational challenges and extending applicability to large, realistic datasets.

Findings

Method achieves unbiased, optimal estimates under squared error loss.

Supports efficient multi-hash sketch frequency estimation.

Validated on synthetic and real datasets, outperforming existing methods.

Abstract

We provide a novel statistical perspective on a classical problem at the intersection of computer science and information theory: recovering the empirical frequency of a symbol in a large discrete dataset using only a compressed representation, or sketch, obtained via random hashing. Departing from traditional algorithmic approaches, recent works have proposed Bayesian nonparametric (BNP) methods that can provide more informative frequency estimates by leveraging modeling assumptions about the distribution of the sketched data. In this paper, we propose a smoothed-Bayesian method, inspired by existing BNP approaches but designed in a frequentist framework to overcome the computational limitations of the BNP approaches when dealing with large-scale data from realistic distributions, including those with power-law tail behaviors. For sketches obtained with a single hash function, our approach is supported by rigorous frequentist properties, including unbiasedness and optimality under a squared error loss function within an intuitive class of linear estimators. For sketches with multiple hash functions, we introduce an approach based on multi-view learning to construct computationally efficient frequency estimators. We validate our method on synthetic and real data, comparing its performance to that of existing alternatives.