On the Stability and Generalization of Triplet Learning
It provides foundational theoretical guarantees for triplet learning, which is incremental but important for applications like face recognition and person re-identification.
This paper tackles the lack of theoretical understanding of generalization in triplet learning by establishing high-probability generalization bounds, achieving excess risk bounds of order O(n^{-1/2} log n) for SGD and RRM, and an optimistic bound of O(n^{-1}) for RRM in low-noise cases.
Triplet learning, i.e. learning from triplet data, has attracted much attention in computer vision tasks with an extremely large number of categories, e.g., face recognition and person re-identification. Albeit with rapid progress in designing and applying triplet learning algorithms, there is a lacking study on the theoretical understanding of their generalization performance. To fill this gap, this paper investigates the generalization guarantees of triplet learning by leveraging the stability analysis. Specifically, we establish the first general high-probability generalization bound for the triplet learning algorithm satisfying the uniform stability, and then obtain the excess risk bounds of the order $O(n^{-\frac{1}{2}} \mathrm{log}n)$ for both stochastic gradient descent (SGD) and regularized risk minimization (RRM), where $2n$ is approximately equal to the number of training samples. Moreover, an optimistic generalization bound in expectation as fast as $O(n^{-1})$ is derived for RRM in a low noise case via the on-average stability analysis. Finally, our results are applied to triplet metric learning to characterize its theoretical underpinning.