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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, thelearning theory foundation of PPL has not been touched in the existing works.In this paper, we try to fill this theoretical gap by investigating thegeneralization properties of PPL. After extending the definitions ofalgorithmic stability to the PPL setting, we establish the high-probabilitygeneralization bounds for uniformly stable PPL algorithms. Moreover, explicitconvergence rates of stochastic gradient descent (SGD) and regularized riskminimization (RRM) for PPL are stated by developing the stability analysistechnique of pairwise learning. In addition, the refined generalization boundsof PPL are obtained by replacing uniform stability with on-average stability.

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