Accurate Analysis of Sparse Random Projections

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).