  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.
