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Estimating Performance for Safe Deployment of Machine Learning Models

Zeju Li, Konstantinos Kamnitsas, Mobarakol Islam, Melanie Roschewitz, Cheng Ouyang, Chen Chen, Ben Glocker

arXiv:2610.29262v1cs.LG

TL;DR

Domain shifts make label-free performance assessment important, but class imbalance and confidence miscalibration complicate reliable estimates. MOVAL uses class-wise calibration and an ensemble of confidence scores to estimate multiple metrics across classification and segmentation. Across tested tasks, the ensemble reduces estimation error versus existing methods and supports fine-grained performance analysis.

  • Problem

    Under domain shifts, performance must be assessed without test labels, while existing methods may be task-specific or rely on global calibration that does not provide comprehensive metrics.

    Source: §1 · p. 2

  • Method

    MOVAL applies class-wise calibration to confidence scores and averages calibrated probabilities from multiple scores to estimate performance metrics.

    Source: §5 · p. 30

  • Results

    Across six tasks and 6,572 test scenarios, MOVAL Ensemble reduces estimation error versus the best-performing existing methods by 36.4% for classification accuracy, 51.2% for 2D segmentation F1-Score, and 52.0% for 3D segmentation F1-Score.

    Source: §5 · pp. 30–31

  • Takeaways & Limitations

    MOVAL Ensemble produces stable estimates across most tested scenarios despite training strategies that alter model behavior, and calibrated confidence supports fine-grained performance analysis.

    Source: §5 · p. 31

    Precision estimates use only positive predictions and ignore false negatives, making MOVAL unsuitable as the sole metric when false positives drive clinical interventions.

    Source: §5 · p. 31

Abstract

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The main challenge in applying deep neural networks to real-world scenarios lies in distributional discrepancies between training and test datasets, often caused by variations in data acquisition conditions. Assessing the performance of pre-trained models without labels is crucial for safety, but this is complicated by deep models' overly optimistic probabilistic outputs, often exacerbated by class imbalances, leading to unreliable predictions. To address these issues, we introduce MOVAL, a novel MOdel eVALuation tool that estimates performance using unlabeled test data. MOVAL incorporates class-wise confidence calibration to adjust model outputs, allowing for the estimation of metrics beyond accuracy and mitigating the detrimental effects of class imbalance on confidence calibration. Additionally, we propose an ensemble approach that combines multiple calibrated confidence scores for a more robust solution. We validate MOVAL on natural and medical image datasets with various acquisition shifts, covering tasks from classification to segmentation. It achieves state-of-the-art results across evaluation metrics such as accuracy, F1-Score, AUC, and more. Furthermore, we demonstrate that MOVAL provides accurate performance estimations at the class, instance, and pixel levels, ensuring the transparent and safe deployment of machine learning models. We provide MOVAL as a deployment tool for monitoring and estimating performance under a range of domain shifts.

1. Introduction

Domain shifts make label-free performance assessment important, while class imbalance and globally calibrated confidence can make estimates incomplete or misleading. MOVAL extends confidence-based estimation across metrics and tasks through class-wise calibration and ensembles.

1.1. Related Works

  • Existing evaluation methods are often task-specific or globally calibrated, while confidence-based methods largely focus on accuracy, which can mislead on imbalanced datasets.Uniform calibration can leave majority-class predictions overconfident and minority-class predictions underconfident, increasing errors in class-wise and instance-wise estimates.Source: §1 · p. 2, §1.1 · pp. 3–4

1.2. Contributions

  • MOVAL estimates model performance without manual labels under domain shifts, using class-wise calibration to reduce between-class bias and extend estimation to F1-Score, sensitivity, precision, and AUC.The paper presents the work as a framework, benchmark, and deployable tool, rather than a fundamentally new calibration algorithm.Source: §1.2 · p. 4
  • MOVAL extends confidence-score estimation beyond classification to 2D and 3D segmentation, and combines multiple scores; experiments span six tasks and 6,572 test settings.The authors report estimation-error reductions of 43% in real-world classification tasks and over 50% in segmentation tasks, with class-, instance-, and pixel-wise indicators.Source: §1.2 · pp. 4–5
  • This paper builds on preliminary MICCAI 2022 work on class-wise calibration, adding estimation beyond accuracy, 2D/3D segmentation, confidence-score ensembles, and an open-source deployment tool.The preliminary work was reported to outperform class-wise calibration baselines such as vector scaling.Source: §1.2 · p. 5

2. Preliminaries: Confidence-Based Model Evaluation

MOVAL estimates target-domain performance from unlabeled test inputs by calibrating model confidence against labeled validation data. Its class-specific calibration addresses imbalanced-class confidence biases and supports metric estimation beyond accuracy.

2.1. Problem Setup

  • MOVAL targets performance estimation on a shifted target domain when test images are available without ground-truth labels, using source-domain validation data to adjust probabilities.The framework estimates accuracy, F1-Score, sensitivity, precision, and AUC from model outputs.Source: §2.1 · p. 6
  • The framework maps logits to metrics through confidence-score computation, calibration, and metric calculation, with parameters optimized per class rather than using one shared adjustment.Calibration parameters are fitted against validation-set metrics; the authors present class-specific optimization as supporting imbalance handling and metrics beyond accuracy.Source: §2.1 · pp. 6–7
  • Metric choice changes what deployment decisions can be assessed: lesion segmentation may require F1-Score and pixel-level analysis, sensitivity for missed lesions, or precision for false-positive reduction.The section notes that accuracy alone is insufficient for brain-lesion segmentation.Source: §2.1 · p. 7

2.2. Accuracy Estimation

  • Raw softmax confidence can produce overly optimistic estimates, so MOVAL calibrates probabilities on validation data before using them to estimate metrics.The calibrated probabilities are then applied to target data; the figure describes the same approach for group-wise metrics under expected domain shifts.Source: §2.2 · pp. 7–8, Figure 1 · p. 8
  • Class imbalance can make majority predictions overconfident and minority predictions underconfident; uniform calibration can leave minority-class estimation errors higher.MOVAL introduces class-specific parameters, and the CIFAR10-LT example reports class-wise alignment and the strongest overall accuracy estimation for its ensemble.Source: §2.2 · pp. 9–10, Figure 2 · p. 9

3. Proposed Method: MOVAL

MOVAL calibrates model confidence and uses the calibrated outputs to estimate performance metrics on unlabeled data. Its class-specific, group-wise, and ensemble components extend this approach across metrics and segmentation tasks.

3. Proposed Method: MOVAL

  • MOVAL computes confidence scores, calibrates them against target metrics, then uses calibrated scores or probabilities to estimate dataset metrics.The framework has confidence-score calculation, model calibration, and metrics computation components.Source: §3 · p. 10

3.1. Class-Specific Temperature Scaling / 3.2. Class-Specific Difference of Confidences

  • Class-specific temperature scaling and difference-of-confidences calibrate samples by predicted class, aligning confidence with class-wise accuracy and reducing majority-class influence.Temperature scaling uses a class-specific parameter; DoC uses a class-specific difference between predicted probability and validation accuracy.Source: §3.1 · p. 11, §3.2 · pp. 11–12

3.3. Class-Specific Average Thresholded Confidence / 3.4. Class-Specific with Average Thresholded Confidence with Temperature Scaling

  • Class-specific ATC learns a threshold for each class, while CS TS-ATC first applies temperature scaling and then the ATC process.ATC estimates accuracy from the proportion of samples whose confidence exceeds a learned threshold.Source: §3.3 · p. 12, §3.4 · pp. 12–13

3.5. Confidence Scores Calculation

  • Entropy and Doctor scores can receive temperature scaling, while Doctor and Energy scores are normalized and clipped to [0, 1].The paper extends calibration to confidence scores derived from logits, including Entropy, Doctor, and Energy.Source: §3.5 · p. 13

3.6. Calibration for Group-Wise Metrics

  • For group-wise metrics, MOVAL estimates calibrated probabilities by fitting temperature scaling or distributing remaining probability across non-maximum classes; it adopts the latter for efficiency.Class-specific parameters are optimized sequentially, starting with the class receiving the most predictions, to minimize validation estimation error.Source: §3.6 · p. 14

3.7. MOVAL Ensemble

  • MOVAL Ensemble separately calibrates multiple models and combines their calibrated probabilities for test-set metric estimation.Different model combinations are selected for different tasks.Source: §3.7 · p. 14

3.8. Performance Estimation for Segmentation Tasks

  • For segmentation, MOVAL treats pixels as dense-classification samples but estimates group-wise metrics over cases or volumes; its estimated F1-Score uses calibrated probabilities.The background class is not calibrated because optimizing it was found to destabilize foreground-class results.Source: §3.8 · pp. 14–15

3.9. Group-Wise Calibration / 3.10. Optimization

  • Group-wise calibration shares class-specific parameters across classes to address scarce minority-class samples; the default grouping uses predicted-class counts.All reported results omit group-wise calibration unless specified; parameter optimization uses bound-constrained methods, with Nelder-Mead as the default.Source: §3.9 · pp. 15–16, §3.10 · p. 16

4. Experiments

The experiments evaluate MOVAL across classification and medical-image segmentation tasks under synthetic and real-world domain shifts. Class-specific variants reduce classification estimation errors across accuracy and other metrics, and show greater advantages over existing standards in segmentation.

4.1. Experimental Setup

  • The experiments train classifiers and segmentation models, calibrate using validation labels, then estimate test-set quality from pre-softmax network outputs.The models use ResNet- and U-Net-based training processes.Source: §4.1 · p. 16

4.2. Datasets

  • Evaluation spans long-tailed CIFAR classification, skin-lesion cohorts, and brain-lesion, prostate, and cardiac MRI segmentation under acquisition and synthetic shifts.The skin-lesion test cohorts are independently collected; MRI evaluations include shifts across scanners or institutions.Source: §4.2 · pp. 17–18

4.3. Class-Wise Performance Alignment / 4.4. Multi-Metric Estimation / 4.5. MOVAL for Segmentation Tasks

  • 6.64 to 5.81 overall accuracy MAE; class-specific variants also reduce F1-Score MAE from 21.25 to 13.95 and show greater advantages over existing standards in segmentation.The segmentation comparison reports average MAE for 2D and 3D tasks; accuracy and AUC were omitted because they often approach 100%.Source: Figure 4 · p. 19, §4.3 · p. 20, §4.4 · p. 21

4.4. Multi-Metric Estimation

  • Across three classification tasks, class-specific variants reduce MAE for sensitivity from 20.40 to 14.96, precision from 31.23 to 26.99, and AUC from 9.19 to 6.04.The F1-Score MAE falls from 21.25 to 13.95.Source: §4.4 · p. 21

4.5. MOVAL for Segmentation Tasks

  • Figure 5 presents MAE between real metrics and estimated results for different methods on 2D and 3D segmentation, comparing original estimation methods with proposed class-specific variants; class-wise calibration is described as even more crucial.Source: Figure 5 · p. 21

2021) segmentation

MOVAL’s class-specific variants and confidence-score ensemble reduce performance-estimation error across classification and segmentation settings. The results also cover advanced training strategies, limited validation data, and class-, instance-, and pixel-level feedback.

2021) segmentation

  • Class-specific variants lower F1-Score MAE from 12.88 to 4.73 for 2D segmentation and from 15.41 to 4.69 for 3D segmentation.Accuracy and AUC evaluations are omitted because they often approach 100% in segmentation.Source: 2021) segmentation · p. 23

4.6. Confidence Scores Ensemble

  • MOVAL Ensemble ranks among top performers across tasks and metrics, best in 7/11 scenarios, and reduces best-existing-method MAE from 7.05 to 3.44 (2D F1-Score) and 16.13 to 7.74 (3D F1-Score).The ensemble combines three estimation methods, most often proposed class-specific variants.Source: §4.6 · pp. 24–25, Figure 7 · p. 24

4.7. Robustness under Training Conditions

  • Across advanced balanced and robust training strategies, MOVAL Ensembles outperform the best-performing existing methods by a substantial margin; group-wise calibration can stabilize accuracy estimation.Group-wise calibration aligns accuracy across groups sharing similar statistics rather than calibrating individual classes.Source: §4.7 · pp. 26–27

4.8. Stability with Varying Amounts of Data

  • For CIFAR10-LT, 5% of validation data yields performance comparable to the best-existing methods on most metrics; stable results need about 60 samples per case, 12 2D slices, or 6 3D volumes.The 12-slice and 6-volume requirements apply to 2D and 3D segmentation, respectively.Source: §4.8 · p. 27

4.9. Informative Indicators at Different Levels

  • MOVAL improves class-wise alignment, more accurately reflects instance-level segmentation performance, and uses pixel confidence maps to highlight poorer-performing classes and uncertain regions.Combined confidence values tend to concentrate near 0 and 1, which may make anomalies easier to detect without carefully crafting a threshold.Source: §4.9 · pp. 28–29, Figure 9 · p. 28, Figure 10 · p. 29

5. Discussion and Conclusion

MOVAL estimates model performance without labels through class-wise calibration and supports multiple metrics across domain shifts. Its ensemble improves estimation in classification and segmentation, while its deployment role remains monitoring support rather than a guarantee of safety.

5. Discussion and Conclusion

  • Class-wise calibration supports accuracy, F1-Score, sensitivity, precision, and AUC estimation while reducing class-related calibration bias and sensitivity to test label-distribution variation.It also extends confidence-based estimation to group-wise metrics.Source: §5 · p. 30
  • Across six tasks and 6,572 test scenarios, MOVAL offers advantages over existing standards and applies to classification, 2D segmentation, and 3D segmentation.The framework can integrate additional confidence scores or performance-estimation methods.Source: §5 · p. 30
  • MOVAL Ensemble reduces estimation error versus existing methods by 36.4% for classification accuracy, 51.2% for 2D segmentation F1-Score, and 52.0% for 3D segmentation F1-Score.It averages calibrated probabilities from multiple estimation methods.Source: §5 · pp. 30–31
  • MOVAL primarily targets medical-imaging acquisition shifts; under more severe shifts that change the confidence-correctness relationship, calibration may not transfer and a small labeled test sample is recommended.The method cannot guarantee safe deployment under arbitrary shifts, and broader evaluation across additional applications, tasks, and architectures remains future work.Source: §5 · pp. 31–33
  • Precision estimates use only positive predictions and omit false negatives, making them less reliable than sensitivity or F1-Score and unsuitable as the sole metric when false positives drive interventions.MOVAL also recommends treating precision estimates as indicative when validation and target prevalence differ substantially or the positive class is extremely rare.Source: §5 · pp. 31–32
  • For classification, about 5% of validation data, or approximately 60 samples per class, can suffice for stable estimates; segmentation typically needs about 12 2D slices or 6 3D volumes.Class-wise calibration is preferred when classes have tens of validation samples; group-wise calibration can use fewer samples per group for rare classes.Source: §5 · p. 33

Appendix A. Quantitative Results

Appendix A reports MAE-based estimation evaluations for classification accuracy and segmentation DSC (F1-Score) across tasks and domain shifts.

Appendix A. Quantitative Results

  • Table A.1 evaluates accuracy estimation for different classification tasks under varied domain shifts using MAE.Bold and underlined entries mark the best and second-best results within each category and configuration.Source: Table A.1 · p. 43
  • Both tables organize comparisons by task and domain-shift configuration, with lower MAE serving as the evaluation basis.The captions identify best and second-best results within each category and configuration, but provide no cell values.Source: Table A.1 · p. 43, Table A.2 · p. 44
  • Table A.2 evaluates DSC (F1-Score) estimation for different segmentation tasks under varied domain shifts using MAE.Bold and underlined entries mark the best and second-best results within each category and configuration.Source: Table A.2 · p. 44

Appendix B. MOVAL API and Example Usage

The API accepts model outputs and validation labels for fitting, then estimates performance on test outputs; the package implements MOVAL algorithms, while separate repositories provide experiment-reproduction materials.

Appendix B. MOVAL API and Example Usage

  • The moval Python package implements confidence scores, calibration, and metric computation for use with trained models, but does not contain the paper’s experiments.Separate scripts and dataset/model repositories contain materials for reproducing the main experiments.Source: Appendix B · p. 45
  • A classification example uses 100 validation samples across 10 classes and 200 test samples, then configures accuracy estimation with Entropy confidence and TS calibration.The example passes logits and ground-truth labels to fit the estimator.Source: Appendix B · p. 45
  • A MOVAL Ensemble can be constructed by selecting an ensemble algorithm, and fitting and inference follow the same pattern across classification and segmentation.The provided example names a classification accuracy ensemble; a separate example configures 3D segmentation with Doctor confidence and CS ATC for F1-Score.Source: Appendix B · p. 46
  • After fitting, estimates can be obtained for test data, while fitted validation performance and calibrated probabilities are also available.The example notes output shapes of one value for accuracy and c values for group-wise metrics; instance-wise estimates have N classification values or Z segmentation values.Source: Appendix B · p. 46
  • The documentation recommends supplying MOVAL with all pretrained models and saving and loading parameters for reuse.Source: Appendix B · p. 47

Appendix C. Supplementary Figures

The supplementary figures depict the study’s datasets and acquisition shifts, compare MOVAL with existing estimation approaches, and illustrate calibration and confidence-score behavior.

Appendix C. Supplementary Figures

  • The figures show datasets spanning long-tailed classification, skin-lesion data from eight sources, and cardiac, prostate, and brain-lesion segmentation from multiple scanners; other panels illustrate acquisition shifts and confidence-score distributions.Figure C.21 describes the MOVAL Ensemble distribution as bimodal near 0 and 1, while Figure C.14 shows training and test intensity histograms for 12 test conditions.Source: Figure C.12 · p. 48, Figure C.13 · p. 49, Figure C.14 · p. 50
  • Figure C.15 compares MAE between real and estimated metrics and shows predicted versus real label distributions for 2D and 3D segmentation.It notes that extreme class-ratio imbalance makes accuracy and AUC less informative because they are close to 100%.Source: Figure C.15 · p. 51
  • Figure C.16 reports MAE comparisons and paired tests for F1-Score, precision, sensitivity, and AUC estimation across classification and segmentation tasks.The caption includes an exception: sensitivity estimation for 2D segmentation has T(68) = −0.26, p = 0.80.Source: Figure C.16 · p. 52
  • Figure C.17 compares MAE across classification tasks for proposed and existing methods, and contrasts original estimation methods with class-specific variants.Its caption describes MOVAL Ensemble as achieving state-of-the-art performance for several classification tasks.Source: Figure C.17 · p. 53
  • Figure C.18 compares MAE for proposed and existing methods across segmentation tasks, including original and class-specific variants.The caption describes MOVAL Ensemble as achieving state-of-the-art performance for several segmentation tasks.Source: Figure C.18 · p. 54
  • Figure C.20 describes group-wise calibration as more robust when validation samples are reduced, while noting possible effects on false-positive estimation and, with sufficient data, AUC and precision.Source: Figure C.20 · p. 55

Appendix D.1. Group-Wise and Class-Specific Metrics Estimation

MOVAL estimates group-wise metrics from predicted probabilities, using predicted labels as test-time substitutes for ground truth. Class-specific calibration adjusts probabilities so estimates align with validation-set metrics.

Appendix D.1. Group-Wise and Class-Specific Metrics Estimation

  • Predicted probabilities, rather than only confidence scores, support group-wise metrics that use information from non-maximum classes.Predicted labels substitute for unavailable test-time ground truth in the calculations.Source: Appendix D.1 · p. 57
  • Reported estimates replace raw probabilities with class-wise calibrated probabilities, while metrics derived from uncalibrated probabilities may be inaccurate.Accuracy calibration alone may be suboptimal because it does not necessarily improve every metric.Source: Appendix D.1 · p. 58
  • Class-specific calibration optimizes metric-specific parameters so estimates align with actual validation-set metrics.MOVAL applies this calibration to group-wise metrics as well as accuracy.Source: Appendix D.1 · p. 58
  • For F1-Score, MOVAL separately calibrates probabilities for predictions of each class and aligns the resulting estimate with that class’s actual metric.Sensitivity and precision are calibrated similarly; AUC uses five equally spaced probability thresholds per class to estimate the area under its FPR–TPR curve.Source: Appendix D.1 · p. 58

Appendix D.2. Network Configurations

The appendix details classification and segmentation network configurations, imbalance-aware training losses, and augmentation strategies. The methods include approaches intended to improve minority-class learning or generalization across domain shifts.

Appendix D.2. Network Configurations

  • Classification experiments use ResNet-32 for CIFAR datasets and ResNet-50 for skin-lesion classification, while segmentation uses a 3D U-Net in nnU-Net.Training schedules and patch sizes vary by task; segmentation patches are sampled from whole images because of memory limitations.Source: Appendix D.2 · pp. 59–60
  • LDAM applies unequal class margins, with larger margins for classes having fewer samples, to focus learning on minority classes.The margin depends on a hyper-parameter and the number of samples in each class.Source: Appendix D.2 · p. 59
  • Deferred re-weighting begins with uniform sample weights and later gives minority classes larger weights based on class frequency.The weight starts at 1 and later becomes 1/n_y.Source: Appendix D.2 · p. 60
  • Cutout improves in-domain accuracy but fails to improve most out-of-domain results, possibly because networks rely more on original intensity distributions.The authors report it because it is a default classification training technique.Source: Appendix D.2 · p. 60
  • Baseline segmentation training uses a balanced sum of cross-entropy and sample-wise soft DSC losses.MRI volumes receive Z-score normalization; networks are trained with SGD using a linearly decreasing learning rate.Source: Appendix D.2 · p. 61
  • Asymmetric large-margin and focal losses modify cross-entropy and soft DSC for rare classes; asymmetric focal loss removes their attenuation term to help prevent minority-class under-fitting.The described segmentation training combines the modified cross-entropy and soft DSC losses with equal weighting.Source: Appendix D.2 · pp. 61–62
  • GIN randomizes image style using a kernel-based transformation and helps generalization across appearances, but performs worse under spatial transformations.The authors exclude spatial-transformation synthetic shifts when evaluating advanced training strategies, including GIN, for fair comparison.Source: Appendix D.2 · p. 62
  • Mixup extends training distributions by combining two samples and their labels using the same interpolation coefficient.The coefficient is sampled from a beta distribution.Source: Appendix D.2 · p. 63

Appendix D.3. Fine-Grained Performance Analysis

The appendix describes how estimation errors and performance visualizations are examined at class, instance, and pixel levels. Evaluation excludes absent test classes and segmentation background.

Appendix D.3. Fine-Grained Performance Analysis

  • Evaluation compares estimated with actual metrics using MAE, averages class-wise MAE across classes, and uses paired t-tests across conditions.Absent test classes are excluded, particularly for skin-lesion classification, and the segmentation background class is omitted.Source: Appendix D.3 · p. 63
  • Class-wise analysis compares average confidence grouped by predicted class with corresponding sample accuracy, while segmentation instance analysis evaluates cases separately.Pixel visualizations show F1-Score-adjusted calibrated confidence, with uncertainty represented as 1 minus that confidence.Source: Appendix D.3 · p. 63

Appendix E. Supplementary Tables

The supplementary tables cover estimation metrics, tasks, training strategies, validation-data amounts, and synthetic segmentation shifts. Their captions provide evaluation scope, while accompanying text identifies group-wise calibration as a response to difficult balanced-training scenarios.

Appendix E. Supplementary Tables

  • The supplementary results span accuracy, sensitivity, precision, F1-Score, and AUC estimation across classification and segmentation tasks.The captions identify tables for varied domain shifts, minority-class-only test sets, and alternative training strategies.Source: Table E.3 · p. 64, Table E.5 · p. 65, Table E.6 · p. 66
  • Additional tables report segmentation accuracy and AUC estimation, and F1-Score estimation for CIFAR10 and brain-lesion segmentation under different training strategies.The captions identify best and second-best results within categories but provide no cell values here.Source: Table E.10 · p. 69, Table E.11 · p. 70, Table E.12 · p. 71
  • For CIFAR10 models using advanced balanced training, proposed class-specific variants underperform counterparts in accuracy estimation.The authors attribute the difficulty to altered predicted probabilities and confusion matrices under shifts, and recommend group-wise calibration or tracking F1-Score.Source: Table E.13 · p. 72
  • Group-wise calibration shares parameters across the eight most-predicted classes and the remaining two, reducing validation-sample requirements and confusion-matrix complexity.The authors state this strategy lets the variants generalize effectively with advanced balanced training strategies.Source: Table E.14 · p. 73
  • Further tables examine ensemble estimation MAE as validation-data amounts vary for CIFAR10 accuracy and cardiac and brain-lesion segmentation F1-Score.The ensemble’s selected confidence scores and the synthetic segmentation transformations are also catalogued.Source: Table E.16 · p. 75, Table E.17 · p. 75, Table E.18 · p. 76
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