Nonparametric Distribution Matching for Self-Supervised Whole-Slide Image Condensation
Organizations: University of Illinois Urbana-Champaign · Washington State University · Hanoi Medical University · VinUniversity · Hanoi University of Science and Technology
Abstract
Histological whole-slide images (WSIs) are central to computational pathology but pose severe computational challenges due to their extremely high resolution, often spanning several gigabytes per slide. To enable scalable learning, existing methods apply self-supervised data condensation to reduce computational cost, but typically rely on heuristic prototype learning and do not explicitly preserve learning-relevant feature distributions for downstream tasks. In response, we introduce a principled reformulation of WSI condensation as a distribution-matching problem under a fixed representational lens, and develop NICER, a tractable approximation framework based on a nonparametric prior with slide-adaptive capacity. Experiments on five histopathology datasets, together with clinical evaluation from a board-certified pathologist, show that NICER consistently outperforms prior methods, achieving an average accuracy improvement of 7.44% while offering improved efficiency-accuracy trade-offs, highlighting the benefits of principled, distribution-aware condensation for scalable histological representation learning. Source codes are available in https://github.com/nmduonggg/NICER.
Figures & tables
| Method | Decoder | Cancer Subtyping | Survival Prediction | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| PANDA | NSCLC | LUAD | BRCA | CPTAC | ||||||
| Kappa | Accuracy | F1 | Kappa | Bal. Acc. | F1 | C-Index | C-Index | C-Index | ||
| Whole Bag | ABMIL | 91.93 ± 0.48 | 76.21 ± 1.53 | 76.37 ± 1.38 | 90.31 ± 1.65 | 94.52 ± 1.19 | 95.19 ± 0.78 | 62.12 ± 1.27 | 78.52 ± 3.82 | 48.26 ± 4.87 |
| DeepSets | 57.26 ± 38.13 | 51.60 ± 17.98 | 46.42 ± 23.91 | 79.51 ± 1.80 | 89.82 ± 0.88 | 89.73 ± 0.91 | 59.89 ± 5.34 | 49.23 ± 3.59 | 49.80 ± 7.96 | |
| ProtoCount | 0.83 ± 9.55 | 24.24 ± 1.21 | 11.77 ± 1.28 | 10.69 ± 3.54 | 55.34 ± 1.78 | 53.86 ± 3.15 | 51.91 ± 5.75 | 56.47 ± 12.03 | 51.72 ± 8.97 | |
| H2T | 75.03 ± 1.08 | 53.91 ± 1.10 | 50.66 ± 1.01 | 79.45 ± 1.80 | 89.67 ± 0.88 | 89.72 ± 0.90 | 51.83 ± 2.59 | 45.86 ± 4.29 | 45.34 ± 0.67 | |
| Metric | Whole Bag | PANTHER | NICER |
|---|---|---|---|
| Storage (GB) | 194 | 3.2 | 5.7 |
| Condense GPU (MB) | - | 5.30 | 9.17 |
| Condense Time (s) | - | 0.05 | 1.51 |
| Mean F1 | 93.58 | 90.69 | 94.23 |
Appendix figures & tables14 assets
Supplementary material from the paper’s appendix.
Appendix
| Theoretical object | Role | NICER approximation |
|---|---|---|
| Empirical slide distribution | Reduced support | |
| Distribution matching | Gaussian pattern-concept likelihood | |
| Cardinality penalty | Active concept set | |
| PPP prior | Variable-capacity prior | Pruning unassigned concepts |
| MAP inference | Prototype selection | Alternating updates over and |
| Method | Predictor | Kappa | Bal. Acc. | F1 |
|---|---|---|---|---|
| OT | ABMIL | |||
| H2T | ||||
| PANTHER | ||||
| NICER (Ours) | ||||
| OT | DSMIL | |||
| H2T |
| Method | Predictor | Kappa | Accuracy | F1 |
|---|---|---|---|---|
| OT | ABMIL | 0.0264 ± 0.0849 | 0.2036 ± 0.0158 | 0.1213 ± 0.0318 |
| H2T | 0.5318 ± 0.1789 | 0.4034 ± 0.0736 | 0.3439 ± 0.1228 | |
| PANTHER | 0.0467 ± 0.1002 | 0.2373 ± 0.0807 | 0.1341 ± 0.0659 | |
| NICER (Ours) | 0.8392 ± 0.0514 | 0.6398 ± 0.0365 | 0.6332 ± 0.0327 | |
| OT | DSMIL | 0.6253 ± 0.0944 | 0.4430 ± 0.0636 | 0.4436 ± 0.0843 |
| H2T | 0.6548 ± 0.0411 | 0.4183 ± 0.0083 | 0.3494 ± 0.0205 |
| PANDA | NSCLC | LUAD (Survival) | BRCA (Survival) |
| 62.80 | 154.67 | 157.40 | 158.60 |
| Method | Config | % Input | F1 |
|---|---|---|---|
| Whole Bag (Upperbound) | - | 100% | 74.42 |
| PANTHER | K=16 | 2.58% | 41.11 |
| K=64 | 10.39% | 55.93 | |
| K=128 | 20.78% | 69.45 | |
| NICER (Ours) | M=50 | 5.79% | 67.64 |
| M=200 | 11.32% | 73.04 |
| Predictor | ABMIL | DSMIL | ILRA | ||||||
|---|---|---|---|---|---|---|---|---|---|
| Top- | Kappa | Acc. | F1 | Kappa | Acc. | F1 | Kappa | Acc. | F1 |
| 1 | 90.18 | 70.02 | 69.87 | 85.42 | 64.65 | 65.95 | 89.17 | 64.88 | 64.24 |
| 3 | 91.48 | 74.94 | 75.00 | 88.73 | 68.46 | 67.52 | 92.25 | 73.83 | 74.55 |
| 5 | 90.47 | 72.93 | 72.72 | 88.80 | 68.46 | 66.66 | 88.66 | 71.36 | 71.47 |
| 10 | 89.52 | 70.47 | 70.49 | 85.42 | 66.89 | 66.94 | 88.88 | 68.90 | 68.92 |
| Method | Head | NSCLC - Match | LUAD-Match | ||
|---|---|---|---|---|---|
| Kappa | Bal. Acc. | F1 | C-Index | ||
| PANTHER | ABMIL | 9.67 ± 3.23 | 54.84 ± 1.59 | 52.51 ± 4.27 | 52.79 ± 10.26 |
| OT | 82.04 ± 2.96 | 91.03 ± 1.54 | 91.02 ± 1.47 | 62.60 ± 2.22 | |
| NICER | 89.73 ± 1.81 | 94.84 ± 0.92 | 94.87 ± 0.91 | 64.67 ± 2.11 | |
| PANTHER | DSMIL | 1.21 ± 2.01 | 48.70 ± 2.66 | 42.41 ± 8.36 | 40.03 ± 3.11 |
| OT | 78.74 ± 12.13 | 89.24 ± 6.15 | 89.20 ± 6.33 | 56.54 ± 1.61 | |
| Method | Head | NSCLC - Max | ||
|---|---|---|---|---|
| Kappa | Bal. Acc. | F1 | ||
| PANTHER | ABMIL | 2.35 ± 5.56 | 51.19 ± 2.80 | 41.52 ± 7.33 |
| OT | 73.84 ± 15.46 | 87.01 ± 7.60 | 86.51 ± 8.41 | |
| NICER | 89.73 ± 1.81 | 94.84 ± 0.92 | 94.87 ± 0.91 | |
| PANTHER | DSMIL | 6.97 ± 0.96 | 53.46 ± 0.47 | 44.10 ± 3.38 |
| OT | 82.06 ± 5.54 | 91.06 ± 2.75 | 91.02 ± 2.78 | |