Stability-based Generalization Analysis for Mixtures of Pointwise and Pairwise Learning

TL;DR

This paper develops a theoretical framework for understanding the generalization properties of mixture algorithms combining pointwise and pairwise learning, providing stability-based bounds and convergence rates.

Contribution

It extends stability analysis to PPL, deriving high-probability generalization bounds and convergence rates for SGD and RRM in this setting.

Findings

Established high-probability generalization bounds for PPL algorithms

Derived explicit convergence rates for SGD and RRM in PPL

Provided refined bounds using on-average stability

Abstract

Recently, some mixture algorithms of pointwise and pairwise learning (PPL) have been formulated by employing the hybrid error metric of "pointwise loss + pairwise loss" and have shown empirical effectiveness on feature selection, ranking and recommendation tasks. However, to the best of our knowledge, the learning theory foundation of PPL has not been touched in the existing works. In this paper, we try to fill this theoretical gap by investigating the generalization properties of PPL. After extending the definitions of algorithmic stability to the PPL setting, we establish the high-probability generalization bounds for uniformly stable PPL algorithms. Moreover, explicit convergence rates of stochastic gradient descent (SGD) and regularized risk minimization (RRM) for PPL are stated by developing the stability analysis technique of pairwise learning. In addition, the refined generalization bounds of PPL are obtained by replacing uniform stability with on-average stability.