Distribution-based deep multiple instance learning for tumor proportion scoring in NSCLC

Artur Bartczak; Jaros{\l}aw Kwiecie\'n; Krzysztof Pysz; Piotr Krajewski; Witold Dyrka

arxiv: 2606.27579 · v1 · pith:FISAA42Gnew · submitted 2026-06-25 · 💻 cs.CV · cs.AI· cs.LG· q-bio.TO

Distribution-based deep multiple instance learning for tumor proportion scoring in NSCLC

Krzysztof Pysz , Artur Bartczak , Jaros{\l}aw Kwiecie\'n , Piotr Krajewski , Witold Dyrka This is my paper

Pith reviewed 2026-06-29 01:31 UTC · model grok-4.3

classification 💻 cs.CV cs.AIcs.LGq-bio.TO

keywords multiple instance learningtumor proportion scoreNSCLCzero-inflated betadigital pathologydeep learningslide level predictiondistribution modeling

0 comments

The pith

A zero-inflated beta distribution model in multiple instance learning predicts tumor proportion scores more accurately than regression methods from slide-level labels alone.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops an end-to-end framework with two components: a network to extract embeddings and classify features from individual tissue patches, and a multiple instance learning model that aggregates those embeddings to estimate parameters of a zero-inflated beta distribution for the tumor proportion score of the entire slide. This uses only the slide-level TPS score as supervision. The approach aims to address the challenge of limited expert annotations for manual TPS assessment in NSCLC by improving both prediction accuracy and the ability to explain results through how concentrated the predicted distribution is. It shows that this distribution-based method significantly outperforms standard linear and ridge regression baselines.

Core claim

By training a distribution-based MIL architecture to predict the parameters of a zero-inflated beta distribution representing TPS, the model achieves higher accuracy than baseline regressions while providing explainability through the concentration of the estimated distribution, all without requiring patch-level annotations.

What carries the argument

The MIL aggregation that outputs parameters of the zero-inflated beta distribution for TPS, which allows the model to represent the probability distribution over possible tumor proportions for a slide.

If this is right

Outperforms linear and ridge regression in prediction accuracy for TPS.
Handles non-expressive zero-class images better due to the zero-inflated component.
Captures expected accuracy through the concentration of the predicted distribution.
Provides improved explainability compared to point-estimate regression methods.
Enables training with only slide-level labels in an end-to-end manner.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The distribution modeling could be applied to other quantitative scoring tasks in digital pathology where proportions are estimated.
Uncertainty in TPS predictions could be derived from the variance of the ZIBeta distribution for clinical decision support.
Reducing reliance on patch-level annotations might accelerate development of similar models for other cancer types.
Integration with existing pathology workflows could decrease the time experts spend on manual scoring.

Load-bearing premise

That tumor proportion scores follow a zero-inflated beta distribution and that aggregating patch embeddings via MIL can reliably estimate the distribution parameters without patch-level supervision.

What would settle it

If on an independent test set the ZIBeta-based model does not show lower error metrics than the ridge regression baseline, or if the distribution concentration does not correlate with prediction accuracy as expected, the performance advantage would be falsified.

Figures

Figures reproduced from arXiv: 2606.27579 by Artur Bartczak, Jaros{\l}aw Kwiecie\'n, Krzysztof Pysz, Piotr Krajewski, Witold Dyrka.

**Figure 1.** Figure 1: Architecture of ZIBeta model In contrast to predicting the canonical shape parameters α and β, this alternative parameterization offers more directly interpretable model outputs, with µ as an approximate predicted value and ν as an indicator of the certainty of a given prediction. The ϕ parameter determines the probability of the outcome being exactly zero, while simultaneously shifting the predicted mean … view at source ↗

**Figure 2.** Figure 2: LOWESS plots showcasing the relationship between predicted concentration (ν) and absolute error of predictions. Blue line denotes median concentration (ν = 8.24) Inset: Distribution of predicted values given the actual label. Red line denotes identity. was relatively close to 50% to ensure that the slide contained a similar number of stained and non-stained tumor patches. The vast majority of the most atte… view at source ↗

**Figure 3.** Figure 3: Randomly sampled patches belonging to low, medium and high scoring attention categories ordered by percentiles. Each category within corresp. 3 × 5 patch area. Immune cells Necrosis Other Stroma Tumor alveoli background b c a d [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

**Figure 4.** Figure 4: Raw image (a) and predicted tissue types (b) for a WSI with TPS label of 60%. Patch-level TPS (c) and attention (d) extracted with the ZIBeta model by randomly sampling unique 4096-sized batches [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

read the original abstract

Accurate assessment of tumor proportion score (TPS) in non-small cell lung cancer (NSCLC) is critical for treatment planning and prognosis. Key challenges include the tedious manual work required to annotate each slide, combined with the limited number of experts certified for this task. Multiple instance learning (MIL) has proven to be an effective approach for predicting TPS scores at the slide level; however, existing methods struggle with non-expressive (zero class) images. Our approach involves two models: (1) an embedding-extraction and multiclass-classification network that captures the histopathological features of individual patches, and (2) a MIL model that aggregates these embeddings to predict zero-inflated beta (ZIBeta) parameters representing the overall TPS probability distribution for the entire slide. Using only slide-level TPS scores as labels, we demonstrate how this end-to-end framework can leverage a novel distribution-based architecture to improve prediction accuracy and explainability. ZIBeta modeling significantly outperforms baseline linear and ridge regression while capturing expected accuracy through distribution concentration.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

ZIBeta MIL for TPS scoring adds a distribution output but the four parameters look hard to identify from slide-level means alone.

read the letter

The new piece here is feeding patch embeddings through a MIL aggregator that directly outputs the four parameters of a zero-inflated beta (zero-inflation probability plus the two shape parameters) rather than a scalar TPS prediction. That framing is the main departure from standard MIL regression for this task.

The setup makes sense on paper: slide-level TPS labels are cheap to get, and modeling the full distribution could in principle give both a point estimate and some measure of concentration or uncertainty. The claim that it beats linear and ridge regression on the same labels is plausible given how simple those baselines are.

The soft spot is identifiability. The only supervision is the expected value of the distribution (the TPS score). Multiple combinations of zero-inflation rate and beta shape parameters can produce the same mean, so nothing in the loss forces the model to recover the actual underlying distribution. Without patch-level labels, synthetic checks, or post-hoc validation that the predicted distributions match observed patch statistics, the extra parameters may just be fitting noise while the mean stays correct. The abstract does not mention any such checks.

The baselines are too weak to tell us whether the distribution modeling itself is doing useful work. A reader would want to see at least one other MIL method and one other distributional head before concluding the ZIBeta choice is responsible for any gains.

This is for people already working on MIL in computational pathology who want probabilistic outputs for scoring tasks. It is not yet clear enough on the central modeling assumption to send out for review without first seeing whether the authors have addressed the parameter recovery issue in the full experiments.

Referee Report

2 major / 2 minor

Summary. The paper proposes an end-to-end distribution-based multiple instance learning (MIL) framework for tumor proportion score (TPS) prediction in NSCLC pathology slides. It consists of a patch embedding and multiclass classification network followed by a MIL aggregator that predicts the four parameters of a zero-inflated beta (ZIBeta) distribution to model slide-level TPS. Using only slide-level TPS labels, the authors claim that ZIBeta modeling significantly outperforms linear and ridge regression baselines in accuracy while improving explainability through distribution concentration.

Significance. If the central results hold, the work would demonstrate a practical way to move from point-estimate MIL to full distributional modeling in weakly supervised computational pathology, which is relevant for zero-inflated proportion data like TPS. The explicit use of a parametric distribution for aggregation is a clear methodological contribution that could aid interpretability.

major comments (2)

[Method (ZIBeta MIL aggregator)] Method section describing the MIL aggregator and ZIBeta parameter prediction: the central claim that the four ZIBeta parameters can be recovered from patch embeddings using only a scalar slide-level TPS target (the mean of the distribution) lacks justification for identifiability. Multiple distinct (π, α, β) combinations can produce identical expected values, so the learned parameters may not correspond to the underlying patch distribution even when the mean matches the label.
[Experiments] Experimental results section: the abstract states outperformance over linear and ridge regression baselines, but the manuscript must provide concrete details on datasets, cross-validation procedure, exact metrics (e.g., MAE, calibration of the full distribution), and statistical significance tests to support the claim that the distributional model improves accuracy beyond mean matching.

minor comments (2)

[Abstract] The abstract should include at least one sentence on the datasets used and the primary evaluation metric to allow readers to assess the scope of the claimed improvement.
[Method] Notation for the ZIBeta parameters (zero-inflation probability and shape parameters) should be defined explicitly when first introduced, and the loss function used to train the parameter predictor should be stated.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address the two major comments point by point below. We will revise the manuscript to incorporate clarifications and additional details where appropriate.

read point-by-point responses

Referee: [Method (ZIBeta MIL aggregator)] Method section describing the MIL aggregator and ZIBeta parameter prediction: the central claim that the four ZIBeta parameters can be recovered from patch embeddings using only a scalar slide-level TPS target (the mean of the distribution) lacks justification for identifiability. Multiple distinct (π, α, β) combinations can produce identical expected values, so the learned parameters may not correspond to the underlying patch distribution even when the mean matches the label.

Authors: We agree that identifiability is a valid concern. The supervision signal is the slide-level mean TPS, so the loss primarily constrains the expected value of the predicted ZIBeta distribution; multiple parameter combinations can yield the same mean. The end-to-end architecture uses patch embeddings to inform the parameter predictions, but this does not guarantee unique recovery of all four parameters. We will revise the method section to explicitly acknowledge this limitation, clarify that the model is not claimed to recover the exact underlying patch distribution, and emphasize that the value lies in improved mean accuracy plus distributional outputs for explainability. We will also add a brief discussion of this point. revision: partial
Referee: [Experiments] Experimental results section: the abstract states outperformance over linear and ridge regression baselines, but the manuscript must provide concrete details on datasets, cross-validation procedure, exact metrics (e.g., MAE, calibration of the full distribution), and statistical significance tests to support the claim that the distributional model improves accuracy beyond mean matching.

Authors: We agree that the experimental section requires more concrete details to support the claims. In the revision we will expand the experiments section to specify the datasets (number of slides, sources, and preprocessing), the cross-validation procedure, the exact evaluation metrics (including MAE for the mean and any distribution calibration measures), and the statistical significance tests performed. These additions will allow readers to assess whether the ZIBeta model provides benefits beyond mean matching. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on standard MIL and external baselines

full rationale

The paper describes an end-to-end MIL architecture that aggregates patch embeddings to predict ZIBeta distribution parameters using only slide-level TPS labels, then compares performance against linear and ridge regression baselines. No quoted equations, self-citations, or steps reduce the central claim to a fitted input renamed as prediction, a self-definitional loop, or a load-bearing uniqueness theorem imported from the authors' prior work. The modeling assumptions (ZIBeta form and MIL aggregation) are stated explicitly as modeling choices rather than derived by construction from the target outputs, leaving the derivation self-contained against the provided external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides insufficient detail to identify specific free parameters, axioms, or invented entities; no equations or implementation specifics are given.

pith-pipeline@v0.9.1-grok · 6719 in / 1034 out tokens · 58191 ms · 2026-06-29T01:31:56.764868+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

13 extracted references · 12 canonical work pages · 1 internal anchor

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Scientific Reports14(1), 7136 (Mar 2024)

van Eekelen, L., Spronck, J., Looijen-Salamon, M., Vos, S., Munari, E., Giro- lami, I., Eccher, A., Acs, B., Boyaci, C., de Souza, G.S., Demirel-Andishmand, M., Meesters, L.D., Zegers, D., van der Woude, L., Theelen, W., van den Heuvel, M., Grünberg, K., van Ginneken, B., van der Laak, J., Ciompi, F.: Comparing deep learning and pathologist quantification...

work page doi:10.1038/s41598-024-57067-1 2024

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Govindan, R., Aggarwal, C., Antonia, S.J., Davies, M., Dubinett, S.M., Fer- ris, A., Forde, P.M., Garon, E.B., Goldberg, S.B., Hassan, R., Hellmann, M.D., Hirsch, F.R., Johnson, M.L., Malik, S., Morgensztern, D., Neal, J.W., Patel, J.D., Rimm, D.L., Sagorsky, S., Schwartz, L.H., Sepesi, B., Herbst, R.S.: Society for immunotherapy of cancer (sitc) clinical...

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, author Sandler, M

Howard, A., Sandler, M., Chu, G., Chen, L.C., Chen, B., Tan, M., Wang, W., Zhu, Y., Pang, R., Vasudevan, V., Le, Q.V., Adam, H.: Searching for MobileNetV3. arXiv (May 2019). https://doi.org/10.48550/arXiv.1905.02244

work page doi:10.48550/arxiv.1905.02244 2019

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Ilse, M., Tomczak, J.M., Welling, M.: Attention-based Deep Multiple Instance Learning. arXiv (Feb 2018). https://doi.org/10.48550/arXiv.1802.04712

work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1802.04712 2018

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Kim, H., Kim, S., Choi, S., Park, C., Park, S., Pereira, S., Ma, M., Yoo, D., Paeng, K., Jung, W., Park, S., Ock, C.Y., Lee, S.H., Choi, Y.L., Chung, J.H.: Clinical Validation of Artificial Intelligence–Powered PD-L1 Tumor Pro- portion Score Interpretation for Immune Checkpoint Inhibitor Response Pre- diction in Non–Small Cell Lung Cancer. JCO Precision O...

work page doi:10.1200/po.23.00556 2024

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Scientific Reports11(1), 15907 (Aug 2021)

Liu, J., Zheng, Q., Mu, X., Zuo, Y., Xu, B., Jin, Y., Wang, Y., Tian, H., Yang, Y., Xue, Q., Huang, Z., Chen, L., Gu, B., Hou, X., Shen, L., Guo, Y., Li, Y.: Automated tumor proportion score analysis for PD-L1 (22C3) expres- sion in lung squamous cell carcinoma. Scientific Reports11(1), 15907 (Aug 2021). https://doi.org/10.1038/s41598-021-95372-1, publish...

work page doi:10.1038/s41598-021-95372-1 2021

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López, L.J.L., Elsharief, S., Jorf, D.A., Darwish, F., Ma, C., Shamout, F.E.: Uncertainty quantification for machine learning in healthcare: A survey (2025), https://arxiv.org/abs/2505.02874

work page arXiv 2025

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appendix b.6

MinistryofHealth,RepublicofPoland:Refundationnoticeno.81(1january2026). appendix b.6. treatment of patients with lung cancer (icd-10: C34) and pleural mesothelioma (icd-10:c45). https://www.gov.pl/attachment/af3ac669-45c2-4875- 9822-e89e9f6612ce (2025), accessed: 2026-01-08

2025

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Journal of Translational Medicine19(1) (Jun 2021)

Pan, B., Kang, Y., Jin, Y., Yang, L., Zheng, Y., Cui, L., Sun, J., Feng, J., Li, Y., Guo, L., Liang, Z.: Automated tumor proportion scoring for PD-L1 expres- sion based on multistage ensemble strategy in non-small cell lung cancer. Journal of Translational Medicine19(1) (Jun 2021). https://doi.org/10.1186/s12967-021- 02898-z, publisher: Springer Science a...

work page doi:10.1186/s12967-021- 2021

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Histopathology87(1), 90–100 (2025)

Plass, M., Olteanu, G.E., Dacic, S., Kern, I., Zacharias, M., Popper, H., Fukuoka, J., Ishijima, S., Kargl, M., Murauer, C., Kalson, L., Brcic, L.: Comparative perfor- mance of pd-l1 scoring by pathologists and ai algorithms. Histopathology87(1), 90–100 (2025). https://doi.org/10.1111/his.15432

work page doi:10.1111/his.15432 2025

[12] [12]

Archives of Pathology & Laboratory Medicine148(7), 757–774 (Jul 2024)

Sholl, L.M., Awad, M., Roy, U.B., Beasley, M.B., Cartun, R.W., Hwang, D.M., Kalemkerian,G.,Lopez-Rios,F.,Mino-Kenudson,M.,Paintal,A.,Reid,K.,Ritter- house, L., Souter, L.A., Swanson, P.E., Ventura, C.B., Furtado, L.V.: Programmed death ligand-1 and tumor mutation burden testing of patients with lung cancer for selection of immune checkpoint inhibitor ther...

work page doi:10.5858/arpa.2023-0536-cp 2024

[13] [13]

MIHIC: a multiplex IHC histopathological image classification dataset for lung cancer immune microenvironment quantification

Wang, R., Qiu, Y., Wang, T., Wang, M., Jin, S., Cong, F., Zhang, Y., Xu, H.: MIHIC: a multiplex IHC histopathological image classification dataset for lung cancer immune microenvironment quantification. Frontiers in Immunology15(Feb 2024). https://doi.org/10.3389/fimmu.2024.1334348, publisher: Frontiers

work page doi:10.3389/fimmu.2024.1334348 2024