Hashing Algorithms for Large-Scale Learning

TL;DR

This paper introduces a method integrating b-bit minwise hashing with learning algorithms like SVM and logistic regression, enabling efficient large-scale learning on high-dimensional, massive datasets, and demonstrates its advantages over existing methods.

Contribution

The paper presents a novel integration of b-bit minwise hashing with linear learning algorithms, improving efficiency and accuracy in large-scale, high-dimensional data scenarios.

Findings

b-bit minwise hashing can be integrated with SVM and logistic regression.

Compared to VW, b-bit minwise hashing is more accurate at the same storage level.

Combining b-bit minwise hashing with VW enhances training speed, especially with larger b.

Abstract

In this paper, we first demonstrate that b-bit minwise hashing, whose estimators are positive definite kernels, can be naturally integrated with learning algorithms such as SVM and logistic regression. We adopt a simple scheme to transform the nonlinear (resemblance) kernel into linear (inner product) kernel; and hence large-scale problems can be solved extremely efficiently. Our method provides a simple effective solution to large-scale learning in massive and extremely high-dimensional datasets, especially when data do not fit in memory. We then compare b-bit minwise hashing with the Vowpal Wabbit (VW) algorithm (which is related the Count-Min (CM) sketch). Interestingly, VW has the same variances as random projections. Our theoretical and empirical comparisons illustrate that usually $b$-bit minwise hashing is significantly more accurate (at the same storage) than VW (and random projections) in binary data. Furthermore, $b$-bit minwise hashing can be combined with VW to achieve further improvements in terms of training speed, especially when $b$ is large.