We study a mini-batch diversification scheme for stochastic gradient descent (SGD). While classical SGD relies on uniformly sampling data points to form a mini-batch, we propose a non-uniform sampling scheme based on the Determinantal Point Process (DPP). The DPP relies on a similarity measure between data points and gives low probabilities to mini-batches which contain redundant data, and higher probabilities to mini-batches with more diverse data. This simultaneously balances the data and leads to stochastic gradients with lower variance. We term this approach Balanced Mini-batch SGD (BM-SGD). We show that regular SGD and stratified sampling emerge as special cases. Furthermore, BM-SGD can be considered a generalization of stratified sampling to cases where no discrete features exist to bin the data into groups. We show experimentally that our method results more interpretable and diverse features in unsupervised setups, and in better classification accuracies in supervised setups.

本文提出了一种基于 Determinantal Point Process（DPP）的新型非均匀采样方案，用于在 mini-batch SGD 优化中实现数据的多样性和平衡，成为了Diversified Mini-Batch SGD (DM-SGD)。实验结果表明，该方法在无监督和监督学习中均能产生更具解释性和多样性的特征，并提高分类准确性。

小批量差异化的行列式点过程