Generalized Cauchy-Schwarz Divergence and Its Deep Learning Applications

TL;DR

This paper introduces the generalized Cauchy-Schwarz divergence (GCSD), a new measure for multiple distributions, with a kernel-based estimator, demonstrating its effectiveness in deep clustering and multi-source domain adaptation tasks.

Contribution

The paper proposes the GCSD, a novel divergence measure for multiple distributions, along with a practical kernel-based estimator, advancing the tools available for complex deep learning applications.

Findings

GCSD outperforms traditional methods in clustering tasks.

GCSD effectively improves multi-source domain adaptation.

Experimental results confirm robustness and efficiency of GCSD.

Abstract

Divergence measures play a central role and become increasingly essential in deep learning, yet efficient measures for multiple (more than two) distributions are rarely explored. This becomes particularly crucial in areas where the simultaneous management of multiple distributions is both inevitable and essential. Examples include clustering, multi-source domain adaptation or generalization, and multi-view learning, among others. While computing the mean of pairwise distances between any two distributions is a prevalent method to quantify the total divergence among multiple distributions, it is imperative to acknowledge that this approach is not straightforward and necessitates significant computational resources. In this study, we introduce a new divergence measure tailored for multiple distributions named the generalized Cauchy-Schwarz divergence (GCSD). Additionally, we furnish a kernel-based closed-form sample estimator, making it convenient and straightforward to use in various machine-learning applications. Finally, we explore its profound implications in the realm of deep learning by applying it to tackle two thoughtfully chosen machine-learning tasks: deep clustering and multi-source domain adaptation. Our extensive experimental investigations confirm the robustness and effectiveness of GCSD in both scenarios. The findings also underscore the innovative potential of GCSD and its capability to significantly propel machine learning methodologies that necessitate the quantification of multiple distributions.