Variational Weakly Supervised Gaussian Processes

Abstract

We introduce the first model to perform weakly supervised learning with Gaussian processes on up to millions of instances. The key ingredient to achieve this scalability is to replace the standard assumption of MIL that the bag-level prediction is the maximum of instance-level estimates with the accumulated evidence of instances within a bag. This enables us to devise a novel variational inference scheme that operates solely by closedform updates. Keeping all its parameters but one fixed, our model updates the remaining parameter to the global optimum. This virtue leads to charmingly fast convergence, fitting perfectly to large-scale learning setups. Our model performs significantly better in two medical applications than adaptation of GPMIL to scalable inference and various scalable MIL algorithms. It also proves to be very competitive in object classification against state-of-the-art adaptations of deep learning to weakly supervised learning.