Understanding Sparse JL for Feature Hashing

Dec 12, 2019

Speakers

About

Feature hashing and other random projection schemes are commonly used to reduce the dimensionality of feature vectors. The goal is to efficiently project a high-dimensional feature vector living in R^n into a much lower-dimensional space R^m, while approximately preserving Euclidean norm. These schemes can be constructed using sparse random projections, for example using a sparse Johnson-Lindenstrauss (JL) transform. A line of work introduced by Weinberger et. al (ICML '09) analyzes the accuracy of sparse JL with sparsity 1 on feature vectors with small linfinity-to-l2 norm ratio. Recently, Freksen, Kamma, and Larsen (NeurIPS '18) closed this line of work by proving a tight tradeoff between linfinity-to-l2 norm ratio and accuracy for sparse JL with sparsity 1. In this paper, we demonstrate the benefits of using sparsity s greater than 1 in sparse JL on feature vectors. Our main result is a tight tradeoff between linfinity-to-l2 norm ratio and accuracy for a general sparsity s, that significantly generalizes the result of Freksen et. al. Our result theoretically demonstrates that sparse JL with s > 1 can have significantly better norm-preservation properties on feature vectors than sparse JL with s = 1; we also empirically demonstrate this finding.

Organizer

Categories

About NIPS 2019

Neural Information Processing Systems (NeurIPS) is a multi-track machine learning and computational neuroscience conference that includes invited talks, demonstrations, symposia and oral and poster presentations of refereed papers. Following the conference, there are workshops which provide a less formal setting.

Like the format? Trust SlidesLive to capture your next event!

Professional recording and live streaming, delivered globally.

Sharing

Recommended Videos

Presentations on similar topic, category or speaker

Interested in talks like this? Follow NIPS 2019