Multiple-InstanceLearning in Medical Imaging: Correlated Chained Gaussian Processes with a Weighted Noisy-OR Likelihood

Whole-slide images and computed tomography scans are commonly decomposed into patches or slices, whereas diagnostic labels are assigned only at the study level, so that which patches or slices support the diagnosis remains unknown. Multiple-instance learning addresses this weakly supervised setting through aggregation functions, which determine how instance-level evidence produces the bag-level prediction. Several probabilistic MIL methods rely on max-based aggregation, which retains only the strongest instance evidence. On the other hand, the standard noisy-OR combines all instance scores, so that the bag probability depends on the product between the bag cardinality and the average instance activation. As a consequence, a slide covered by thousands of benign patches can receive the same probability as one containing a small tumor region. We introduce Correlated Chained Gaussian Processes with Weighted Noisy-OR Likelihood (CCGP-WNOR), a framework in which each instance is assigned a weight that modulates its contribution to the bag probability, with the weights summing to one so that the aggregation is normalized. Consequently, the bag probability lies between the minimum and maximum instance scores, and a value close to one requires at least one instance carrying strong positive evidence. Instance scores and aggregation weights are obtained by transforming two latent functions coupled through a semiparametric latent factor model with shared Gaussian processes, permitting cross-output dependence in the prior. Posterior uncertainty is propagated through a factorized approximation that preserves marginal means and variances but omits cross-output and cross-instance covariances from likelihood integration and prediction. Scalable inference is performed using inducing variables and stochastic variational inference. Experiments on a semi-synthetic benchmark and three medical imaging datasets show that CCGP-WNOR achieves a competitive performance among the compared state-of-the-art MIL methods.