Generalization bound for kernel similarity learning

TL;DR

This paper establishes generalization bounds for kernel-based similarity learning by analyzing the Rademacher complexity, showing that the bounds depend on the radii of the feature and target spaces.

Contribution

It introduces a novel Rademacher complexity bound for similarity learning formulated as a regression problem in feature spaces.

Findings

High probability bounds depend on the maximum of the radii of the input and output spaces.

Provides theoretical guarantees for the generalization error in kernel similarity learning.

Bridges similarity learning with Rademacher complexity analysis in a regression framework.

Abstract

Similarity learning has received a large amount of interest and is an important tool for many scientific and industrial applications. In this framework, we wish to infer the distance (similarity) between points with respect to an arbitrary distance function $d$. Here, we formulate the problem as a regression from a feature space $\mathcal{X}$ to an arbitrary vector space $\mathcal{Y}$, where the Euclidean distance is proportional to $d$. We then give Rademacher complexity bounds on the generalization error. We find that with high probability, the complexity is bounded by the maximum of the radius of $\mathcal{X}$ and the radius of $\mathcal{Y}$.