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

Prateek Mittal, Ayush Srivastava, Joohi Chauhan

arXiv:2608.23574v1q-bio.QMcs.CVcs.ITcs.LG

TL;DR

WSI patch selection must reduce redundancy and computational cost despite slide-level supervision and task-specific or quality-agnostic existing strategies. InfoDPP-PAC combines teacher-seeded GP relevance, information-theoretic diversity, submodular greedy selection, and PAC-style adaptive stopping. On 202 HISTAI gastrointestinal WSIs, it reduced patches by 83.7% while retaining 97.9% of full-budget composite selection quality, without claiming downstream diagnostic improvement.

  • Problem

    Existing WSI patch-selection strategies do not jointly provide label-free task-relevant quality, mutual-information-grounded diversity, and probabilistically adaptive patch counts.

  • Method

    InfoDPP-PAC combines teacher-seeded Gaussian process relevance modelling, determinantal log-determinant diversity, submodular greedy optimisation, and concentration-based adaptive stopping.

  • Results

    83.7% fewer patches on average retained 97.9% of full-budget composite selection quality, while matched-budget selection achieved significantly higher mean teacher-derived patch quality than all 14 baselines.

  • Takeaways & Limitations

    The results validate InfoDPP-PAC as a controlled quality-diversity-cardinality patch-selection framework.

  • Takeaways & Limitations

    The theory certifies residual information from a seeded surrogate, and experiments validate selection quality rather than downstream diagnostic performance.

Abstract

from arXiv · show

Each WSI slide contains thousands of candidate tissue patches, while supervision is usually available only at slide level. Existing bag-construction strategies like Uniform extraction and handcrafted heuristics do not control redundancy while 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. 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 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.

1 Introduction

InfoDPP-PAC frames patch selection as a quality-diversity-cardinality problem for weakly supervised WSI analysis, combining GP relevance, information-theoretic diversity, greedy optimisation, and adaptive stopping.

  • Uniform extraction retains every supra-threshold patch, wasting computation on redundant morphological regions.
  • Attention-based MIL couples patch importance to a downstream supervised task, while coreset methods provide embedding-space coverage without modelling task-relevant quality.
  • InfoDPP-PAC combines teacher-seeded GP relevance modelling, determinantal log-determinant diversity, submodular greedy optimisation, and concentration-based adaptive stopping.
  • Theorem 1 identifies log det(I + βK_S) with GP mutual information between selected patch observations and the latent relevance function.
  • Theorems 2–4 show the joint objective is monotone submodular and support a (1−e−1) greedy approximation under cardinality or knapsack budgets.
  • Theorem 6 stops selection when residual information is below a user-specified tolerance with probability at least 1−δ, making patch count slide-dependent.

2 Related Work

Related work spans uniform extraction, task-specific attention, adaptive acquisition, GP information gain, DPPs, and coresets, but the paper positions InfoDPP-PAC as combining quality, diversity, and adaptive stopping.

  • MIL systems such as ABMIL and CLAM learn task-specific attention during training rather than selecting patches independently of the downstream classifier.
  • Existing approaches do not connect selection quality to mutual information, provide a principled stopping criterion, or evaluate selection separately from classifier training.
  • Theorem 1 transfers the GP information-gain and log-determinant equivalence from sensor placement to patch selection using teacher pseudo-labels.
  • InfoDPP-PAC additionally combines information gain with an explicit quality score and derives a concentration-based PAC stopping rule.
  • Coreset methods target training-distribution coverage without modelling a latent relevance function or grounding coverage information-theoretically through a GP.
  • Pathology DPP sampling has explored patch diversity without coupling selection to a quality model.

3 Notation and Preliminaries

The preliminaries define Gaussian-process relevance modelling, determinantal diversity, submodularity, and the kernel notation used by InfoDPP-PAC.

  • Gaussian Processes: A Gaussian Process is specified by a positive-definite kernel, with posterior mean μ_i and standard deviation σ_i at each patch.
  • Determinantal Point Processes: A DPP assigns subset probability proportional to det(K_S), which equals the squared feature-space volume and therefore represents geometric diversity.
  • Submodularity: A set function is submodular when adding an element yields no larger marginal gain to a larger set; monotonicity means additions do not decrease value.
  • Notation: The notation K_S denotes the kernel restriction to S, k_i,C the kernel column between element i and set C, and κ_ii the diagonal kernel value.

4 The InfoDPP-PAC Framework

InfoDPP-PAC models patch quality with a teacher-seeded GP, selects patches using a blended quality-diversity objective, and returns selected patches plus a residual summary of the unselected pool.

  • Problem formulation: The framework represents a WSI as embedded patches and seeks a subset maximising a joint quality-diversity objective under computational costs.
  • Problem formulation: The quality score combines normalised GP posterior mean and uncertainty, balancing exploitation of estimated relevance with exploration of uncertain regions.
  • Teacher-seeded GP: A teacher model supplies relevance pseudo-labels on a small seed set, enabling GP fitting without patch-level annotations.
  • Inference: GP posterior quantities are evaluated across all patches, with Nyström approximation reducing the stated cost from O(nm_0^2) to O(nr^2).
  • Greedy selection: Greedy selection adds the feasible patch with the largest blended marginal gain, while Cholesky updates evaluate information marginals incrementally.
  • Stopping: Selection uses blended quality and diversity, whereas stopping uses the largest remaining information-gain marginal to certify residual information.
  • Residual information vector: The output contains the selected subset and a quality-weighted centroid of unselected patches, but the residual vector is not evaluated for end-to-end classification.

5 Theoretical Analysis

The theoretical analysis establishes the log-determinant objective as Gaussian-process information gain, proves monotone submodularity for greedy selection, and derives a probabilistic stopping certificate for residual information. These guarantees depend on seed-stability assumptions and concern the surrogate’s information estimates rather than downstream diagnostic performance.

  • Information-theoretic foundation: Theorem 1 identifies log det(I + βK_S) with the mutual information between selected observations and the latent patch-relevance function.The equivalence holds under a Gaussian process relevance model with Gaussian observation noise and any positive-definite kernel.
  • PAC stopping guarantee: The adaptive procedure stops when the estimated maximum residual information gain falls below a tolerance adjusted by a concentration bound.The stopping rule uses a union-bounded McDiarmid inequality over candidates and greedy steps.
  • Submodularity: Theorem 2 shows that the information objective and the blended quality-information objective are monotone submodular.The information marginal equals conditional mutual information, which decreases as the selected set grows.
  • Greedy guarantees: Theorem 3 provides a (1 −e−1) greedy approximation guarantee under a cardinality constraint for the blended objective.The guarantee follows from monotone submodularity and non-negativity at the empty set.
  • Scope and assumptions: The certificate applies to residual mutual information estimated by the seeded GP, not downstream diagnostic performance or arbitrary MIL clinical utility.Its validity requires the finite-sample seed-stability condition in Assumption 1.
  • PAC stopping guarantee: With probability at least 1−δ, halted selections leave every feasible unselected patch with target information marginal at most τ +2ϵk⋆+1,n.The certificate also bounds the cumulative residual information for comparison sets through submodularity.

6 Experiments

Experiments evaluate InfoDPP-PAC as a patch-selection framework using subset-quality metrics across diversity, coverage, relevance, redundancy, and adaptive cardinality. Adaptive stopping substantially reduces patches while preserving composite quality; fixed-budget comparisons show strongest performance on teacher-derived relevance, with coreset methods stronger on diversity and composite metrics.

  • Evaluation design: The study evaluates subset construction rather than downstream diagnostic accuracy, measuring diversity, coverage, relevance, redundancy, and composite quality.The evaluation explicitly treats these metrics as evidence about selected-set properties, not substitutes for retrained MIL diagnostic performance.
  • Dataset and setup: Experiments use 202 HISTAI gastrointestinal whole-slide images, with 76–4,000 filtered tissue patches per slide and a mean of 2,075 patches.Teacher relevance pseudo-labels are derived from cosine similarity to training-split category prototypes and used to fit the GP quality model.
  • Adaptive stopping: 83.7% fewer patches are processed on average by adaptive stopping than the fixed 300-patch budget, while retaining 97.9% of full-budget composite score.Across 22 held-out test slides, stopping points range from 6 to 179 patches and all stop before the 300-patch cap.
  • Fixed-budget comparison: At fixed k = 50, InfoDPP-PAC achieves the highest mean patch quality, 1.518, while farthest-point and k-center greedy obtain higher log-det values, 20.82 and 20.77 versus 12.60.The coreset methods also achieve higher composite scores, 0.604 and 0.596 versus 0.588, reflecting a quality–diversity trade-off.
  • Ablation study: Removing DPP increases redundancy by 33% and reduces log-det diversity by 26%, while quality rises slightly from 1.440 to 1.483.This supports a trade-off: quality-only greedy selection repeatedly favors high-quality clusters and sacrifices non-redundancy.
  • Ablation study: Using only posterior mean or variance lowers quality to 0.807 or 0.861 versus 1.440, whereas the Nyström variant remains within one standard deviation of the full-kernel model.The results support the combined exploitation–exploration score and indicate robustness to kernel approximation and, more modestly, kernel choice.

7 Discussion

The discussion positions InfoDPP-PAC as a quality-diversity-cardinality selector whose strongest empirical advantage is adaptive efficiency, while delimiting claims about diagnostic performance, generalisation, teacher validity, and computational cost.

  • Empirical implications: At k = 50, InfoDPP-PAC leads mean patch quality, whereas farthest-point sampling and k-center greedy achieve higher log-det diversity.This reflects the framework’s intended quality-diversity trade-off rather than optimisation of diversity alone.
  • Methodological interpretation: Separating the blended selection marginal from the residual-information stopping marginal is central to the validity of the PAC certificate.The blended gain chooses the next patch, while the maximum residual information-gain marginal certifies saturation.
  • Limitations and scope: The main evidence comes from one gastrointestinal dataset; a seven-slide-per-organ pilot suggests similar adaptive behaviour in breast and colorectal data but cannot support a general multi-organ claim.A pre-specified multi-organ benchmark with organ-stratified confidence intervals and interaction tests is identified as the needed closure.
  • Limitations and scope: The evaluation validates selection quality rather than downstream diagnosis, so it does not establish improved AUC, F1, or calibration after retraining MIL models.The proposed closure is an end-to-end comparison using multiple aggregators under matched compute, splits, and hyperparameter-search budgets.
  • Limitations and scope: Teacher-derived relevance inherits the coverage and bias of prototype labels, while exact GP inference remains costly for slides exceeding 10^5 candidates or large multi-resolution pools.The paper mitigates these issues through auditable mappings, separate diversity and redundancy reporting, scaling approximations, and implementation optimisations, but leaves them open.

8 Conclusion

InfoDPP-PAC unifies Gaussian process relevance modelling, determinantal diversity, and adaptive stopping for WSI patch selection, with an information-theoretic interpretation of its objective. On 202 HISTAI gastrointestinal whole-slide images, it reduced patch processing while preserving composite selection quality, without claiming downstream diagnostic improvement.

  • InfoDPP-PAC unifies Gaussian process relevance modelling, determinantal log-determinant diversity, and concentration-based adaptive stopping in one submodular patch-selection framework.
  • The log-determinant diversity criterion corresponds to Gaussian process mutual information between selected patch observations and a latent relevance function.
  • 83.7% fewer patches were processed on average than under a fixed full budget while retaining 97.9% of full-budget composite selection quality.
  • At matched budgets, InfoDPP-PAC achieved higher mean teacher-derived patch quality than all 14 baselines, with diversity and composite scores close to the strongest coreset methods.
  • The results support InfoDPP-PAC as a quality-diversity-cardinality patch selector rather than a downstream diagnostic predictor.
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