Stability-based Generalization Analysis for Mixtures of Pointwise and Pairwise Learning
This provides theoretical guarantees for PPL algorithms used in feature selection, ranking, and recommendation, but it is incremental as it extends existing stability analysis to a hybrid setting.
The paper tackles the lack of theoretical foundation for mixtures of pointwise and pairwise learning (PPL) by investigating their generalization properties, establishing high-probability generalization bounds and explicit convergence rates for algorithms like SGD and RRM.
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.