InfoDPP-PAC: Principled Patch Selection for Whole Slide Image Analysis

Whole-slide image (WSI) analysis is limited by a familiar mismatch: each slide contains tens of thousands of candidate tissue patches, while supervision is usually available only at slide level. Existing bag-construction strategies tend to address only one side of this problem. Uniform extraction and handcrafted heuristics do not control redundancy, attention-based multiple-instance models couple patch importance to a particular downstream classifier, and coreset methods optimise embedding-space coverage without modelling task-relevant patch quality. We introduce InfoDPP-PAC, a principled patch-selection framework that combines teacher-seeded Gaussian process relevance modelling, determinantal log-determinant diversity, submodular greedy optimisation, and a concentration-based adaptive stopping rule. The main theoretical result shows that the log-determinant diversity term used in DPP-style selection is the Gaussian process mutual information between a selected subset and the latent relevance function. This yields a monotone submodular objective with standard greedy approximation guarantees at fixed budgets. We further derive a PAC-style certificate for residual information gain, allowing the number of retained patches to vary by slide rather than being fixed a priori. The empirical study is deliberately scoped to selection-quality validation: it evaluates whether the selected subset is diverse, spatially and morphologically covering, non-redundant, and enriched for the teacher-derived relevance signal. It does not claim end- to-end diagnostic improvement after retraining a downstream MIL model. On 202 HISTAI gastrointestinal whole-slide images, the adaptive rule uses 83.7% fewer patches on average than a fixed full budget while retaining 97.9% of full-budget composite selection quality. At a matched budget, InfoDPP-PAC achieves the highest mean teacher-derived relevance score among fourteen baselines, with diversity and composite scores close to the strongest coreset methods. The results support InfoDPP-PAC as a controlled quality-diversity-cardinality selection framework, rather than as a downstream clinical predictor.