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REVIEW 2 major objections 4 minor 25 references

RegScore: Scoring Systems for Regression Tasks

T0 review · 2 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read RegScore shows that sparse, interpretable scoring systems can be built for regression tasks and can match black-box accuracy when estimating mean pulmonary artery pressure.

desk verdict A genuinely new but incremental idea—regression scoring systems and personalized CLS-token heads—whose main claims depend on a preprocessing pipeline that must be nested inside CV to be trusted. read the letter →

arxiv 2507.19155 v1 pith:3QRNYU4M submitted 2025-07-25 eess.IV

Michal K. Grzeszczyk , Tomasz Szczepański , Pawel Renc , Siyeop Yoon , Jerome Charton , Tomasz Trzciński , Arkadiusz Sitek This is my paper · ORCID
classification eess.IV
keywords scoringsystemsinterpretableregressionsparseridgebeamsearchpulmonaryhypertensionmeanarterypressuremultimodaldeeplearningcardiacMRI
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to establish that scoring systems—the simple point-based tools clinicians already use for classification—can be built directly for regression tasks without sacrificing accuracy. To do so, it relaxes the integer-only constraint of classical scoring systems and fits a k-sparse ridge regression on discretized features, producing RegScore. It then shows how to make bimodal deep learning models interpretable by using the transformer's learned representation to generate per-sample regression weights (PLR) or per-sample sparse scores (PRS). On the task of estimating mean pulmonary artery pressure from clinical records and cardiac MRI, the paper reports that RegScore matches or exceeds black-box models while remaining fully transparent. If this holds, clinicians could get continuous, trustworthy predictions with a visible decision rule instead of choosing between accuracy and interpretability.

What carries the argument

The load-bearing object is the k-sparse ridge regression on a binarized feature matrix, expressed as $\min_\beta \|y - \hat X \beta\|_2^2 + \lambda_2 \|\beta\|_2^2$ subject to $\|\beta\|_0 \le k$, which forces the final score to depend on at most k binary conditions. Beam search (adapted from FasterRisk) and OKRidge are the two solvers; the beam-search version assumes that a good size-k model contains a good size-(k−1) model, while OKRidge uses branch-and-bound with lower bounds. For the personalized variants, the machinery shifts to the CLS token of the TIP transformer: a linear layer turns the CLS token into N+1 per-sample weights for PLR, and a gating function with a top-k selection turns it into a sparse per-sample score for PRS.

What would settle it

Rerun the 5-fold cross-validation with discretization and feature selection recomputed inside each training fold, using the same test folds, and compare MAE and F1; if the numbers shift by more than the reported standard deviations, the reported generalization advantage is partly an artifact of leakage.

Watch

Extended reading notes

Core claim

RegScore is a sparse, interpretable scoring system for regression: continuous and categorical features are first binarized by discretization (MDLP or tertiles), then a k-sparse ridge regression minimizes squared error while using at most k binary features, with the weights solved by beam search or by the OKRidge branch-and-bound algorithm. On the study's dataset, both variants reach a mean absolute error of about 7.73–7.75 mmHg for mean pulmonary artery pressure, and the same score thresholded at 25 mmHg outperforms the classification scoring systems RiskSLIM, MISS, and FasterRisk in accuracy and F1. For bimodal data, the paper uses the CLS token of a TIP transformer—the learned representation token—to generate personalized linear regression weights per patient (PLR), or to gate the binarized features so that only the top-k contribute to a per-patient score (PRS). PRS achieves the highest F1 of 93.84% among all compared methods, edging out the full black-box TIP model, while PLR stays within 0.3 mmHg of TIP's mean absolute error. The paper's claim is that these sparse, transparent models are competitive with, and sometimes better than, state-of-the-art black-box models.

Load-bearing premise

The results assume that discretization bins, missing-value thresholds, and f-regression feature selection are all fitted on the training folds alone and never on the held-out test set, a detail the paper does not explicitly confirm.

Editorial extensions

If this is right

  • RegScore returns a continuous mPAP estimate in mmHg, so a clinician can see exactly which binarized features (e.g. septal angle, reveal score) add or subtract points from the baseline 40.5 mmHg.
  • At both k=5 and k=50, RegScore outperforms the classification scoring systems RiskSLIM, MISS, and FasterRisk on PH classification, with the differences reaching statistical significance.
  • PRS reaches the best F1 among all models compared, including black-box multimodal transformers, while remaining interpretable through its per-patient feature gates.
  • RegScore can be trained in about 55 seconds, making it practical to generate and inspect many sparse models before choosing one.
  • Larger model sizes k improve both regression and classification performance of RegScore, giving an explicit dial for the interpretability-accuracy trade-off.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper's ablations show that switching the discretization method (MDLP vs tertiles) degrades performance, so the method's success on a new dataset will likely depend on choosing a binning strategy matched to that data.
  • PLR's per-sample weight vectors could be mined for patient-level feature importance or subgroup patterns, a use the paper only gestures at with mean weights.
  • A direct test of the claimed generalizability would be to apply RegScore to other continuous clinical endpoints defined by thresholds—for example, ejection fraction or laboratory values—and check whether the accuracy-interpretability balance persists.
  • Because the paper does not state explicitly that every preprocessing step is refit inside each cross-validation fold, rerunning the pipeline with fold-local discretization and feature selection is a needed check on the size of the reported advantage.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. The paper introduces RegScore, a sparse and interpretable scoring system for regression, obtained by solving a k-sparse ridge regression on binarized tabular features using either beam search (FasterRisk-style) or OKRidge. It then extends this idea to bimodal deep learning by using the CLS token of the TIP transformer to generate Personalized Linear Regression (PLR) weights and a Personalized RegScore (PRS) with a gating mechanism. The method is evaluated on the ASPIRE dataset for estimating mean pulmonary artery pressure (mPAP) and for pulmonary hypertension classification, with comparisons against classical scoring systems, tabular machine learning models, and deep multimodal baselines. The paper claims that RegScore, PLR, and PRS achieve performance comparable to or better than state-of-the-art black-box models while providing interpretability, and it provides a public code repository.

Significance. If the empirical results withstand scrutiny, the contribution is meaningful: it extends interpretable scoring systems from classification to regression, introduces a way to make bimodal deep-learning predictions more transparent through personalized linear scoring, and demonstrates the approach on a clinically relevant dataset with a public code release. The formulations in Section 2 are simple and consistent, and the paper includes ablations, comparisons against multiple baselines, and example scores in Table 4. However, the central empirical claim currently depends on evaluation details that are not fully specified, and the reported margins over many baselines are small; therefore, the significance of the contribution hinges on whether the evaluation protocol is confirmable as leakage-free.

major comments (2)
  1. [Section 3, Implementation details] The manuscript does not state that f-regression feature selection, MDLP/tertile discretization, and standardization are fitted only on each training fold. Because f-regression uses the mPAP labels and MDLP uses target information, fitting these steps on the full 1790-sample training set before the 5-fold split would leak validation-fold information into training, and fitting them on all 2051 samples would leak test information; either would optimistically bias the metrics in Tables 1 and 2. This concern is load-bearing because the headline margins are small (e.g., PRS F1 93.84 versus TabAttention 93.59; RegScoreOKR MAE 7.73 versus GBR 7.67 and RF 7.61). The authors should specify the exact preprocessing pipeline and re-run the experiments with all target-dependent preprocessing nested inside each cross-validation fold.
  2. [Section 3, Implementation details and Tables 1-2] The sentence 'Mean and standard deviation are reported across the test set over five folds' is ambiguous, and the paired t-test p-values appear to compare five fold-trained models on the same 261 test samples. If the same test set is evaluated five times, the paired observations are not independent, so a paired t-test on five folds does not support the claim of a statistically significant difference. The significance claims in Section 4 (e.g., 'RegScore outperformed other scoring systems on the classification task (p-value <0.05)') therefore need either an appropriate test with independent units or a correction for the multiple comparisons across baselines, and the number of independent test observations used for testing should be reported.
minor comments (4)
  1. [Table 1] The phrase 'Webold' appears to be a typo for 'We bold', and several numerical entries have inconsistent spacing (e.g., '66.05± 21.5').
  2. [Section 3, Comparison with state-of-the-art methods] The main text refers to 'Gradient Boosting Decision Trees (GBDT)' but Table 2 labels the method 'GBR'; please unify the naming.
  3. [Section 2, Personalized RegScore (PRS)] Equation (3) defines the gating scores and soft/hard gates, but the text does not fully specify how the gated binary features are combined with personalized weights to produce the final prediction; one clarifying sentence would improve reproducibility.
  4. [Figure 2] The right panel begins with an apparent stray label 'Mean i' before the feature names; this should be cleaned up, and the feature abbreviations should be defined in the caption or text.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: RegScore, PLR, and PRS are supervised models trained and evaluated on held-out splits; self-citations appear only as comparison baselines.

full rationale

The paper's central claim is empirical: RegScore minimizes Eq. (1), a sparse ridge regression objective on binarized tabular features, using beam search or OKRidge, and is evaluated on a 261-sample held-out test set with 5-fold cross-validation on a separate 1790-sample training set. Nothing in Eq. (1) or in the beam-search/OKRidge optimization encodes the reported MAE or F1 values; those are measured, not derived. PLR and PRS are supervised heads trained on the CLS token of TIP, and their predictions are linear combinations of tabular features with network-generated coefficients, again evaluated on the held-out test set against external or prior baselines. Self-citations (MISS, TabMixer, TabAttention) are used as baseline comparisons rather than as justification for the method's validity, and TIP itself is an external method. No fitted parameter is renamed as a prediction, no uniqueness theorem is imported from the authors' prior work, and no ansatz is smuggled in via self-citation. The stated limitation in Section 4, that interpretable models reduce regression performance relative to TIP, qualifies the abstract's 'comparable or better' wording but is an inconsistency, not circularity. The possible issue that MDLP/tertile bins or f-regression feature selection may have been fit outside the cross-validation loop is a correctness or leakage concern, not a circular reduction by construction; it does not make the reported prediction equal to the training input by definition.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central method is an empirical model fit, not a derivation. The listed hyperparameters are chosen by hand or grid, the PRS gating mechanism is a learned component, and the evaluation relies on several domain assumptions about the dataset and preprocessing. No new physical entities are introduced.

free parameters (6)
  • k (model size) = 5 and 50
    Sparsity budget in Equation 1; chosen by experiment and ablated in Figure 2.
  • lambda2 (ridge regularization) = 1e-8
    Ridge regularization in Equation 1; effectively no shrinkage, chosen by hand.
  • B (beam search width) = 10
    Beam search width for the FasterRisk-adapted RegScore variant; chosen without sensitivity analysis.
  • tau (soft gating temperature) = 0.1
    Steepness of the sigmoid in Equation 3; chosen by hand and not swept in sensitivity analysis.
  • Discretization choice = MDLP for RegScore, tertiles for PRS
    Different binning strategies are used for the two variants; the ablation shows MDLP helps RegScore but tertiles are kept for PRS.
  • PH classification threshold = 25 mmHg
    mPAP > 25 mmHg is used as the positive class, even though the Introduction cites a 20 mmHg diagnostic threshold; this changes the classification task.
assumptions (5)
  • domain assumption Beam search nesting assumption: a model of size k inherently contains one of the best models of size k-1.
    Stated in Section 2 as the basis of the beam search variant; it is a heuristic, not a guarantee.
  • domain assumption Sparse ridge regression with binary features captures clinically meaningful mPAP relationships.
    Section 2 defines RegScore as a solution to Equation 1 on binarized features; this assumes the binarization retains enough information.
  • domain assumption The CLS token from TIP contains sufficient information to generate per-patient regression weights and gates.
    Section 2 uses the CLS token as the input to PLR and PRS heads without an interpretability analysis of the token itself.
  • domain assumption ASPIRE registry mPAP measurements are accurate and representative for PH scoring.
    All experiments rely on invasively measured labels from a single referral registry; generalization to other centers is assumed.
  • domain assumption Preprocessing steps do not use test information.
    Section 3 does not explicitly state that MDLP or tertile binning and f-regression feature selection are nested inside folds; the paper's evaluation depends on this.

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Cite this review

Pith. "Pith review of RegScore: Scoring Systems for Regression Tasks." pith.science (2026). https://pith.science/paper/3QRNYU4M

@misc{pith2026250719155,
  author       = {Pith},
  title        = {Pith review of: RegScore: Scoring Systems for Regression Tasks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3QRNYU4M}},
  note         = {Machine review of arXiv:2507.19155}
}
read the original abstract

Scoring systems are widely adopted in medical applications for their inherent simplicity and transparency, particularly for classification tasks involving tabular data. In this work, we introduce RegScore, a novel, sparse, and interpretable scoring system specifically designed for regression tasks. Unlike conventional scoring systems constrained to integer-valued coefficients, RegScore leverages beam search and k-sparse ridge regression to relax these restrictions, thus enhancing predictive performance. We extend RegScore to bimodal deep learning by integrating tabular data with medical images. We utilize the classification token from the TIP (Tabular Image Pretraining) transformer to generate Personalized Linear Regression parameters and a Personalized RegScore, enabling individualized scoring. We demonstrate the effectiveness of RegScore by estimating mean Pulmonary Artery Pressure using tabular data and further refine these estimates by incorporating cardiac MRI images. Experimental results show that RegScore and its personalized bimodal extensions achieve performance comparable to, or better than, state-of-the-art black-box models. Our method provides a transparent and interpretable approach for regression tasks in clinical settings, promoting more informed and trustworthy decision-making. We provide our code at https://github.com/SanoScience/RegScore.

Figures

Figures reproduced from arXiv: 2507.19155 by the authors.

Figure 1
Figure 1. Given the tabular (Xt ) dataset, we produce the discretized set (Xˆt ) to create RegScore with beam search or OKRidge (a). We further leverage the TIP method [4] with imaging data (Xi ) (b) to compute CLS token for every sample and create interpretable regression predictions with PLR (c) and PRS (d). scoring system for regression tasks, (2) we present PLR and PRS, two approaches for generating interpretable predicti… view at source ↗
Figure 2
Figure 2. Performance comparison of classification (left) and regression (center) [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

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Reviewed August 15, 2026 · model on record in the stance chip above.