Accurate Analysis of Sparse Random Projections

TL;DR

This paper provides a rigorous analysis of sparse random projections, offering sharp tail bounds that improve numerical guarantees while maintaining simplicity, advancing the understanding of dimensionality reduction techniques.

Contribution

It introduces a novel, simpler analytical approach to derive sharp tail bounds for sparse random projections, matching theoretical limits.

Findings

Sharp sub-Poissonian tail bounds established

Numerical guarantees surpass previous analyses

Analysis technique resembles Bennett's Inequality

Abstract

There has been recently a lot of research on sparse variants of random projections, faster adaptations of the state-of-the-art dimensionality reduction technique originally due to Johsnon and Lindenstrauss. Although the construction is very simple, its analyses are notoriously complicated. Meeting the demand for both simplicity and accuracy, this work establishes sharp sub-poissonian tail bounds for the distribution of sparse random projections. Compared to other works, this analysis provide superior numerical guarantees (exactly matching impossibility results) while being arguably less complicated (the technique resembles Bennet's Inequality and is of independent interest).