This paper considers a novel application of deep AUC maximization (DAM) for multi-instance learning (MIL), in which a single class label is assigned to a bag of instances (e.g., multiple 2D slices of a CT scan for a patient). We address a neglected yet non-negligible computational challenge of MIL in the context of DAM, i.e., bag size is too large to be loaded into {GPU} memory for backpropagation, which is required by the standard pooling methods of MIL. To tackle this challenge, we propose variance-reduced stochastic pooling methods in the spirit of stochastic optimization by formulating the loss function over the pooled prediction as a multi-level compositional function. By synthesizing techniques from stochastic compositional optimization and non-convex min-max optimization, we propose a unified and provable muli-instance DAM (MIDAM) algorithm with stochastic smoothed-max pooling or stochastic attention-based pooling, which only samples a few instances for each bag to compute a stochastic gradient estimator and to update the model parameter. We establish a similar convergence rate of the proposed MIDAM algorithm as the state-of-the-art DAM algorithms. Our extensive experiments on conventional MIL datasets and medical datasets demonstrate the superiority of our MIDAM algorithm.

翻译：本文探讨了深度AUC最大化（DAM）在多实例学习（MIL）中的创新应用——在此类学习中，单个类别标签被分配至整个实例包（例如患者CT扫描中的多个二维切片）。我们解决了DAM框架下MIL中一个被忽视但不可忽略的计算挑战：由于实例包规模过大，标准MIL池化方法所依赖的反向传播过程无法将全部数据加载至GPU内存。为应对该挑战，我们基于随机优化思想，将池化预测的损失函数形式化为多层复合函数，提出了方差缩减的随机池化方法。通过融合随机复合优化与非凸极小极大优化技术，我们构建了统一的、可证明的多实例DAM（MIDAM）算法，该算法采用随机平滑最大池化或基于随机注意力的池化，仅对每个实例包采样少量实例即可计算随机梯度估计量并更新模型参数。我们证明了所提MIDAM算法与当前最先进的DAM算法具有相似的收敛速率。在传统MIL数据集与医学数据集上的大量实验验证了MIDAM算法的优越性。