BRIDGE: An Acceptance Gate to Block False Improvements in Model Updates, with a Retrospective Clinical Evaluation
Organizations: Department of Informatics, Faculty of Intelligent Electrical and Informatics Technology, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia
Abstract
Models are updated repeatedly, and an update that looks better on validation data but not on new data is a false improvement that can misguide clinical decisions. The naive rule accepts every positive validation gain and is optimistic when the same data choose and judge the update. BRIDGE is a model-agnostic acceptance gate that decides each update from predictions and the available labels, with fixed settings. Each fold of the data judges the update chosen on the other folds (cross-fitting) to reduce selection bias; acceptance requires the gain's lower bootstrap bound to exceed a margin. The four settings are (A) 11 new datasets, (B) synthetic tasks, (C) 12 retrospective clinical tasks, and (D) 39 supporting datasets. The false-improvement rate falls from 19.1% (naive) to 1.1% (BRIDGE) in (A), 20.7% to 1.7% (B), 20.0% to 0% (C), and 12.5% to 0.5% (D); every 95% confidence interval of the reduction over datasets or tasks excludes zero (not over the clinical sources). An equal-size random draw from the naive acceptances contains more false improvements in (A)-(E) (post hoc, p<0.001). On the OpenML collection (E) of 14 new datasets, the false-improvement rate falls from 25.6% to 1.0%. BRIDGE removes 97% to 100% of the false improvements that the naive rule accepts, and its mean gain per deployed update is 1.8 to 3.1 times the naive rule's. The 95% upper bound on the false-improvement rate is below 5.5%: formal in (B) for independent tasks (3.56%), and conditional on the real data tested (0.33% to 5.40%).
Figures & tables
| Method | What it controls | Accounts for selection | Labels needed at decision | Bound covers |
|---|---|---|---|---|
| Nested CV and bias corrections [ 13 , 14 , 35 ] | error-estimate optimism | yes (inside estimate) | existing labels only | selection procedure |
| McNemar / cv / corrected [ 21 , 22 , 23 ] | fixed-pair difference | no | existing labels only | prespecified comparison |
| Learn then Test [ 30 ] | policy risk | yes | reserved calibration set | selected policy |
| Update approval [ 19 , 24 ] | bio-creep | yes (within policy) | labeled deployment stream | approval policy |
| No-regression certificates [ 26 , 27 ] | per-slice regression | yes (within slices) | certification set (Zhang); disagreements only (Balachandran) | deployed model |
| BRIDGE | false-improvement rate among accepted updates | yes (per-fold separation) | existing training labels only | acceptance procedure, population-level |
| Parameter | Value |
|---|---|
| Cross-fit folds | |
| Bootstrap replicates | |
| Lower quantile | |
| Margin | |
| Base learner | HGB, library defaults with at most 300 iterations and early stopping |
| Bagged base models | bags of of SEARCH |
| Symbol / term | Definition |
|---|---|
| Task | One dataset, or one draw from the synthetic population . |
| Trial | One re-randomization of the training rows, the SEARCH/POOL split, and the bag draw under a fresh seed; produces one decision; trials per task: (real), (clinical), (multiclass), ( ). |
| Decision; index | Accept or reject in one trial; runs over trials on real data and over tasks on ; is the number of trials or tasks. |
| Source | Clinical: data provider (six sources; the four National Health and Nutrition Examination Survey (NHANES) tasks form one source, the four Behavioral Risk Factor Surveillance System (BRFSS) tasks another). Non-clinical: the dataset. |
| Locked reference | Rows set aside once per task with a pre-registered seed; used only as the ground truth to judge the deployed update. Size: Appendix B . |
| TRAIN SEARCH POOL | SEARCH fits the base models; POOL holds the evidence for selection and gating. Size: Appendix B . |
| Symbol / term | Definition |
|---|---|
| Cross-fitted triple counts: label, baseline prediction, and candidate prediction on each held-out fold, pooled over the folds. | |
| , | Metric difference (candidate minus baseline) from the pooled counts; is one of multinomial bootstrap draws. |
| Accept rule | Accept if and only if ; otherwise retain . |
| Margin | on the scale of the selected metric, not rescaled; for net benefit ( 10 ), five additional net true positives per examples. |
| Any higher-is-better metric computed from a confusion table (weighted , balanced accuracy, macro- , , and, in the binary clinical protocol, net benefit); is the metric, distinct from the accepted count (Section III-D ). |
| Symbol / term | Definition |
|---|---|
| Metric difference between the deployed configuration and on the locked reference. | |
| False improvement, | : the deployed configuration does not improve the selected metric on the locked reference; ties count as false improvements. |
| Clearly worse / reference-uncertain | From the Bayesian-bootstrap interval of [ 66 ] : a Dirichlet posterior over the confusion cells with pseudocount (the Jeffreys prior) on the binary and clinical protocols and over the positive cells on multiclass, draws, quantiles and ; entirely below = clearly worse; entirely above = clearly improving; otherwise reference-uncertain. |
| ; false-improvement rate | if decision accepts; , defined when . |
| Yield; total gain | Accepted updates per decisions; . |
| False-improvement rate among accepted updates, , on the i.i.d. task population . |
| Symbol / term | Definition |
|---|---|
| Naive rule | Accept whenever the configuration selected on the whole of POOL improves the validation metric, i.e., ( 1 ) with a positive gain. |
| McNemar | Exact one-sided binomial test on discordant pairs (candidate correct and baseline wrong, or the reverse) on POOL; tests per-example accuracy. |
| cv | Dietterich’s paired statistic, d.f., on the fixed predictions of the final configuration over five -fold splits of POOL, without refitting. |
| Corrected | Ten – splits of POOL, Nadeau–Bengio variance correction, d.f., final configuration; with re-selection: the candidate is re-chosen inside each split. |
| Fixed margin | Accept when the validation gain on POOL is at least ; pre-registered from development, other post hoc. |
| Random control | Accept at random with BRIDGE’s yield. |
| Setting | Naive false % | BRIDGE false % | Reduction (pp) | False removed % | Gain per update |
|---|---|---|---|---|---|
| (A) New datasets | 19.1 | 1.1 | 18.0 | 99 | 2.5 |
| (B) Synthetic | 20.7 | 1.7 | 19.0 | 97 | 2.1 |
| (C) Clinical | 20.0 | 0.0 | 20.0 | 100 | 1.8 |
| (D) Supporting | 12.5 | 0.5 | 12.0 | 99 | 2.1 |
| (E) OpenML † | 25.6 | 1.0 | 24.6 | 99 | 3.1 |
| No. | Test ( ) | Result | Decision on ( ) and meaning |
|---|---|---|---|
| 1 | T1 ( 14 ) | BRIDGE lower by to pp ( ) | Rejected in (A)–(E): BRIDGE accepts fewer false improvements than the naive rule in every collection |
| 2 | T1 ( 14 ) | BRIDGE lower by to pp wherever is rejected | Rejected in (A), (B), (D), and against the cv test in (C): BRIDGE accepts fewer false improvements |
| 3 | T1 ( 14 ) | These rules have to false improvements; BRIDGE is pp lower than the re-selection test in (D) | Not rejected (except that test in (D)): these rules share the principle of BRIDGE, separating the data that choose from the data that judge; BRIDGE accepts to times as many updates as the holdouts (Section IV-C ) |
| 4 | T1 ( 14 ) | BRIDGE lower by to pp in (A), (B), (D); no difference in (C) | Rejected in (A), (B), (D): the margin lowers the false-improvement rate; in (C) both versions accept almost no false improvement |
| 5 | T2 ( 15 ) | All comparisons within pp ( ) | Rejected in (A)–(D): rejecting this means that the margins are equivalent, so the false-improvement rate is stable across margins in this range |
| 6 | T3 ( 16 ), post hoc | Random draw to false improvements, BRIDGE to ( ) | Rejected in (A)–(E): BRIDGE picks fewer false improvements than a random choice, also within single datasets in (D) and (E) |
| Rule | (A) | (B) | (C) | (D) | (E) |
|---|---|---|---|---|---|
| Naive (validation improves) | 19.1 ∗ | 20.7 ∗ | 20.0 ∗ | 12.5 ∗ | 25.6 ∗ |
| McNemar, same POOL | 12.0 ∗ | 34.8 ∗ | 0.0 ∘ | 6.7 ∗ | – |
| McNemar, cross-fit | 8.9 | 26.0 | 0.0 ∘ | 2.5 ∗ | – |
| cv paired | 6.3 ∗ | 5.6 ∗ | 2.5 ∗ | 3.6 ∗ | – |
| Corrected resampled | 6.3 ∗ | 5.7 ∗ | 2.6 ∘ | 4.2 ∗ | – |
| Corrected , re-selection | 2.3 ∘ | 3.0 ∘ | 0.4 ∘ | 1.5 ∗ | – |
| (A) 11 new datasets | (B) Synthetic | (C) Clinical | (D) Supporting | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Rule | False % | Yield | False % | Yield | False % | Yield | False % | Yield | ||||
| Corrected , re-selection | 2.3 ∘ | 31.7 | 29.8 | 3.0 ∘ | 37.9 | 35.9 | 0.4 ∘ | 58.4 | 56.4 | 1.5 ∗ | 39.6 | 35.2 |
| Holdout 2/3 + 1/3 | 1.3 | 13.9 | 13.4 | 1.9 | 18.6 | 18.0 | 0.0 ∘ | 41.1 | 41.0 | 0.3 ∘ | 19.5 | 18.8 |
| Holdout 1/2 + 1/2 | 3.2 | 17.3 | 16.2 | 2.1 | 24.2 | 23.3 | 0.0 ∘ | 46.0 | 46.0 | 0.8 ∘ | 22.3 | 21.2 |
| Fixed margin, dataset held out † | 5.8 | 31.5 | 28.7 | 4.2 | 49.4 | 45.4 | – | – | – | – | – | – |
| BRIDGE | 1.1 | 25.8 | 24.9 | 1.7 | 33.9 | 32.8 | 0.0 | 50.0 | 49.9 | 0.5 | 30.1 | 29.1 |
| Rule | Accepted | False | Bound % | Yield/100 | Criterion |
|---|---|---|---|---|---|
| Naive (validation improves) | 1,323 | 274 | 23.52 | 94.50 | |
| McNemar on same POOL | 135 | 47 | 45.19 | 9.64 | |
| McNemar on cross-fit | 50 | 13 | 42.65 | 3.57 | |
| cv paired | 610 | 34 | 8.14 | 43.57 | |
| Corrected resampled | 774 | 44 | 7.95 | 55.29 | |
| Corrected , re-selection | 531 | 16 | 5.19 | 37.93 |
| Metric | Naive false impr. % | BRIDGE accepted | BRIDGE false impr. % | Bound % | LOCO- source % |
|---|---|---|---|---|---|
| Co-primary (pre-registered) | |||||
| Net benefit, | 20.0 | 1,199 | 0.0 | 0.33 | 0.50 |
| Balanced accuracy | 0.3 | 2,273 | 0.4 | 0.82 | 1.25 |
| Secondary | |||||
| Weighted | 23.6 | 435 | 2.1 | 5.12 | 7.84 |
| 0.0 | 2,379 | 0.0 | 0.16 | 0.24 | |
| Known as | Cross-fit | Bootstrap bound | Margin | (A) | (B) | (C) | (D) | (E) | |||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| False % | Bound % | False % | Bound % | False % | Bound % | False % | Bound % | False % | Bound % | ||||
| Naive | – | – | – | 19.08 | 22.90 | 20.71 | 23.52 | 19.99 | 22.68 | 12.49 | 14.19 | 27.65 | 32.13 |
| Fixed margin | – | – | 10.20 | 14.17 | 16.42 | 19.19 | 2.65 | 4.05 | 6.18 | 7.68 | 16.74 | 22.48 | |
| Same-POOL bootstrap | – | – | 6.96 | 10.70 | 6.61 | 8.95 | 2.67 | 4.06 | 4.87 | 6.33 | 13.73 | 19.16 | |
| Same-POOL cell | – | 2.65 | 5.85 | 3.18 | 5.14 | 0.00 | 0.31 | 1.08 | 2.06 | 3.37 | 8.17 | ||
| Cross-fit, point | – | – | 10.81 | 15.00 | 12.07 | 14.72 | 7.69 | 9.84 | 7.28 | 8.89 | 18.98 | 24.82 | |
Appendix figures & tables32 assets
Supplementary material from the paper’s appendix.
Appendix
| Dataset | Domain | Source | N | Min. % | Ref. |
|---|---|---|---|---|---|
| (A) 11 new datasets | |||||
| pc3 | Software | OpenML 1050 | 1,563 † | 10.24 | 468 |
| MIC | Medical | OpenML 45648 | 1,649 † | 15.59 | 494 |
| Marketing_Campaign | Marketing | OpenML 46940 | 2,240 † | 14.91 | 672 |
| Pumpkin_Seeds | Agriculture | OpenML 46951 | 2,500 † | 48.00 | 750 |
| seismic-bumps | Mining | OpenML 46956 | 2,584 † | 6.58 | 775 |
| Task | Population | Outcome | Predictors / timing | Hypothetical action |
|---|---|---|---|---|
| mammography | Screening mammograms (OpenML 310) | Malignant calcification | Image-derived features at reading | Recall for biopsy |
| actg175 | HIV-1 trial participants (UCI 890) | Recorded event: CD4 decline , AIDS, or death | Baseline covariates only | Intensify monitoring |
| nhanes_* | US adults 20 y, NHANES 2017–18 | Self-reported: hypertension, diabetes, asthma, CHD | Exam & questionnaire, same visit | Refer for testing |
| brfss_* | US adults, BRFSS 2015 | Self-reported: stroke, asthma, kidney disease, depression | Survey responses, same interview | Refer for screening |
| covid_mx | Confirmed COVID-19 patients, Mexico | In-hospital/registered death | Admission data (comorbidities, triage) | Escalate care |
| wids_icu | ICU admissions, GOSSIS (WiDS 2020) | Hospital death | First-24 h ICU measurements | Escalate care |
| Check | Acc./ false | Bound % | LOCO % | Yield |
|---|---|---|---|---|
| MINI-02 34 (D) 100 | ||||
| frozen gate, threshold-only HGB | 586 / 1 | 1.24 | 1.45 | 17.2 a |
| MINI-04 34 (D) 100 | ||||
| threshold-only KNN, cross-fit gate | 150 / 7 | 14.04 | 19.95 | 4.4 |
| MINI-09 18 dev. 100 | ||||
| third member KNN | 218 / 3 | 5.71 | 8.70 | 12.1 |
| Run | Fixed beforehand | End. | Outcome |
|---|---|---|---|
| 01–19 | mechanism studies; thresholded HGB, HGB–DT ensembles, the space | Beh | validation–test independence hypothesis not supported |
| 04 | threshold-only KNN with the cross-fit gate | Crt | fails (bound ) |
| 09 | third ensemble member: KNN or SVC | Yld | SVC chosen: higher yield at a comparable false-improvement rate |
| 12, 14 | Optuna-tuned HGB on SEARCH | Dsc | small gains; clearly worse in up to of trials, so the fixed configuration is frozen |
| 17, 20 | / / training rows (17 dev.); fresh seeds | Crt | pass (bound / / ) |
| 21 | new binary datasets, weighted- | Crt | pass (bound , LOCO ) |
| Choice | Made with | Assessed on |
|---|---|---|
| Model type and hyperparameters | fixed a priori , no tuning (rationale: Section III-A ) | — |
| Candidate space ( binary default) and gate parameters | development datasets, frozen | families of new data never seen in development (new binary, new multiclass, clinical, fresh synthetic); the confirmation datasets of (D) with fresh seeds |
| Preprocessing (imputation, scaling, encoding) | fitted per bag, SEARCH only; WiDS category codes are listed from all rows before the split (covariates only, no labels) | POOL and reference |
| Base models (up to bag draws, kept bags averaged); early stopping | SEARCH (internal bag validation) | POOL and reference |
| Candidate selection inside the gate | of POOL | the held-out of POOL |
| Accept / reject | lower bootstrap quantile of the cross-fit counts | — |
| Parameter | Value | Set | Tested in |
|---|---|---|---|
| Cross-fit folds | Dev | on (Table D7 ) | |
| Replicates | , multinomial over the triple counts | Dev | MC error, seeds; (Table C1 ) |
| Lower quantile | , decision statistic (not the error level ) | Dev | / / (Tables D7 , D5 ) |
| Margin | Dev | – (Tables D3 , D4 ) | |
| HGB base learner | lr , iter., leaves, /leaf, no L2; early stop: iter., of bag | Lib | tuned HGB (Tables H13 , D6 ) |
| Bags | draws of of SEARCH; kept if every class (multiclass ); averaged | Dev | , , bags on (Table C1 ) |
| Setting | (default) | |||
|---|---|---|---|---|
| (A), weighted- | 357/4: 3.83 / 5.10 | 284/3: 4.23 / 5.95 | 234/2: 4.32 / 6.36 | 209/1: 3.74 / 5.67 |
| (A), balanced accuracy | 856/1: 0.80 / 0.91 | 848/1: 0.81 / 0.92 | 836/0: 0.46 / 0.53 | 825/0: 0.47 / 0.54 |
| (A), macro- | 852/0: 0.45 / 0.52 | 829/0: 0.47 / 0.53 | 813/0: 0.48 / 0.55 | 794/0: 0.49 / 0.56 |
| (A), feature selection, KNN | 263/5: 6.06 / 9.75 | 225/1: 3.45 / 6.00 | 193/0: 2.30 / 4.20 | 169/0: 2.66 / 5.32 |
| (A), feature selection, SVC | 296/10: 8.20 / 11.52 | 253/7: 7.74 / 11.41 | 211/5: 7.73 / 12.22 | 171/3: 7.42 / 12.61 |
| (D) 26, 1,000 rows | 648/12: 4.06 / 4.71 | 558/6: 3.04 / 3.59 | 468/4: 2.91 / 3.52 | 404/3: 2.93 / 3.64 |
| Margin | Acc./false | , pp [95% CI] | TOST | Acc. ratio |
| (A) | ||||
| 0.0025 | 357 / 4 | +0.06 [-0.29; +0.35] | 0.011 | 1.26 |
| 0.0075 | 234 / 2 | -0.20 [-0.88; +1.78] | 0.0498 | 0.82 |
| 0.01 | 209 / 1 | -0.58 [-1.40; +0.04] | 0.0498 | 0.74 |
| (B) | ||||
| 0.0025 | 529 / 10 | +0.21 [-0.22; +0.81] | 1.11 | |
| (A) | ||||
| 2.5% | 299/3, 3.99 eq. | 243/2, 4.15 n.e. | 202/1, 3.89 n.e. | 164/0, 2.76 n.e. |
| 5% | 357/4, 3.83 eq. | 284/3, 4.23 def. | 234/2, 4.32 n.e. | 209/1, 3.74 n.e. |
| 10% | 422/11, 5.94 n.e. | 357/4, 3.83 eq. | 297/3, 4.02 eq. | 251/2, 4.00 n.e. |
| (D) | ||||
| 2.5% | 1,180/7, 1.52 eq. | 972/5, 1.52 eq. | 799/2, 1.17 eq. | 669/0, 0.61 eq. |
| Design | Naive | BRIDGE | Bound | LOCO | LOCO 0 | Crit. |
| (A) | ||||||
| Paper | 1,064 / 203 (19.1) | 284 / 3 (1.1) | 4.23 | 5.95 | 2.11 | |
| Tuned HGB | 1,061 / 246 (23.2) | 211 / 5 (2.4) | 7.73 | 10.66 | 3.02 | |
| baseline change, points: +0.30 [+0.04; +0.61] | ||||||
| Gate tuned | 1,064 / 203 (19.1) | 299 / 2 (0.7) | 3.30 | 4.59 | 1.97 | |
| (D) | ||||||
| Variant | Acc. | False | , % | Cons., % | Yield | Gain |
|---|---|---|---|---|---|---|
| , | 382 | 2 | 2.00 | 2.45 | 27.3 | 13.81 |
| , | 445 | 4 | 2.47 | 4.41 | 31.8 | 15.09 |
| , | 548 | 10 | 3.59 | 5.50 | 39.1 | 16.89 |
| , | 406 | 4 | 2.70 | 3.08 | 29.0 | 14.34 |
| , (standard) | 475 | 8 | 3.56 | 4.70 | 33.9 | 15.61 |
| , | 563 | 16 | 4.90 | 6.24 | 40.2 | 17.12 |
| MIC | Mktg | Census | Homes. | Sant. | |
| POOL rows | 741 | 741 | 1,800 | 1,800 | 1,800 |
| Features | 104 | 25 | 41 | 297 | 369 |
| Fit bags on SEARCH (s) | 1.39 | 0.73 | 1.30 | 6.19 | 4.24 |
| Naive selection (s) | 0.006 | 0.006 | 0.006 | 0.007 | 0.007 |
| Cross-fitted selection (s) | 0.017 | 0.017 | 0.019 | 0.019 | 0.019 |
| Bootstrap (s) | 0.011 | 0.011 | 0.010 | 0.009 | 0.006 |
| Dataset | Naive | Corr. | Re-sel. | No-m. | BRIDGE | |
|---|---|---|---|---|---|---|
| Census-KDD | 100/0 | 60/0 | 86/0 | 40/0 | 55/0 | 17/0 |
| Homesite | 99/3 | 49/0 | 71/0 | 41/0 | 53/0 | 30/0 |
| KDD98 | 83/54 | 7/3 | 8/6 | 3/3 | 2/1 | 0/0 |
| LICD | 100/0 | 79/0 | 90/0 | 79/0 | 86/0 | 72/0 |
| MIC | 100/1 | 75/0 | 96/1 | 72/1 | 82/1 | 71/1 |
| Marketing | 100/0 | 78/0 | 98/0 | 81/0 | 87/0 | 76/0 |
| Comparator | , pp [95% CI] | Holm | |
|---|---|---|---|
| Real data (11 new datasets) | |||
| naive | 0.0002 † | 0.0012 † | |
| McNemar, same POOL | 0.0026 | 0.0078 | |
| cv | 0.0006 | 0.0024 | |
| corrected | 0.0002 | 0.0010 | |
| BRIDGE without margin | 0.0046 | 0.0092 | |
| Learner | AUC | Log-loss | Extreme, % | wF1 | Rounds | Fit, s |
|---|---|---|---|---|---|---|
| HGB | 0.578 | 0.675 | 0.00 | 0.552 | 16.67 | 0.028 |
| XGBoost, default | 0.566 | 0.810 | 1.68 | 0.559 | 300.00 | 0.350 |
| XGBoost, regul. | 0.579 | 0.673 | 0.00 | 0.520 | 7.50 | 0.032 |
| Source | Identity key | Rows | Unique keys | Dup. |
| WiDS 2020 (GOSSIS) | patient_id | 91,713 | 91,713 | 0 |
| one row per patient | ||||
| unique encounter_id: 91,713 | ||||
| hospitals: 147 | ||||
| COVID-19 Mexico | id (record id) | 566,602 | 563,201 | 3,401 |
| duplicates are excess rows | ||||
| Source or subset | BRIDGE | Unc. | Bound | Cons. | LOCO | Naive |
|---|---|---|---|---|---|---|
| Net benefit, (co-primary) | ||||||
| ACTG 175 | 198/0 | 2 | – | – | – | 200/0 |
| BRFSS (4 tasks) | 210/0 | 0 | – | – | – | 684/282 |
| COVID-19 Mexico | 200/0 | 0 | – | – | – | 200/0 |
| Mammography | 10/0 | 1 | – | – | – | 200/0 |
| NHANES (4 tasks) | 401/0 | 1 | – | – | – | 782/171 |
| Dataset | Source | N | K | Feat. | Naive | BRIDGE |
| (E) OpenML datasets | ||||||
| airline-satisfaction | OML 46920 | 129,880 | 2 | 21 | 99/6 | 22/0 |
| KDDCup09-churn | OML 1112 | 50,000 | 2 | 230 | 80/62 | 0/0 |
| bank-marketing | OML 1461 | 45,211 | 2 | 16 | 100/0 | 53/0 |
| pulsar-HTRU2 | OML 45558 | 17,898 | 2 | 8 | 97/45 | 0/0 |
| jm1 | OML 1053 | 10,885 | 2 | 21 | 100/2 | 63/0 |
| Setting | Decisions | Naive: accepted | Naive % false [95% CI] | BRIDGE: accepted | BRIDGE % false [95% CI] | Reduction, pp [95% CI] | Upper bound or (%) | False removed % [95% CI] |
|---|---|---|---|---|---|---|---|---|
| (A) 11 new datasets | 1,100 | 1,064 | 284 | 4.23 | 99 [95; 100] | |||
| (B) Synthetic tasks | 1,400 | 1,323 | 475 | 3.56 | 97 [95; 99] | |||
| (C) Clinical tasks, net benefit | 2,400 | 2,266 | 1,199 | 0.0 | 0.33 | 100 [100; 100] | ||
| (D) 39 supporting datasets | 3,700 | 3,562 | 1,113 | 1.47 | 99 [97; 100] | |||
| (E) OpenML collection, 14 datasets | 1,280 | 1,236 | 192 | 5.40 | 99 [98; 100] |
| Test | Comparison (T1: BRIDGE minus) | (A) | (B) | (C) | (D) | (E) |
|---|---|---|---|---|---|---|
| T1 ( 14 ) | Naive | ( ) | ( ) | ( ) | ( ) | ( ) |
| McNemar, same POOL | ( ) | ( ) | ( ) | ( ) | – | |
| McNemar, cross-fit | – | – | ( ) | ( ) | – | |
| cv paired | ( ) | ( ) | ( ) | ( ) | – | |
| Corrected resampled | ( ) | ( ) | ( ) | ( ) | – | |
| Corrected , re-selection | ( ) | ( ) | ( ) | ( ) | – |
| Rule | Acc- epted | False (%) | Bound % | LOCO % | Yield /100 | Gain /100 | 95% CI, pp |
|---|---|---|---|---|---|---|---|
| (A) 11 new datasets, 1,100 decisions | |||||||
| Naive | 1,064 | 203 (19.1) | 22.90 | 25.27 | 96.7 | 59.5 | [ ; ] ∗ |
| McNemar, POOL | 183 | 22 (12.0) | 24.52 | 30.68 | 16.6 | 12.5 | [ ; ] ∗ |
| McNemar, cross-fit | 45 | 4 (8.9) | 41.14 | 54.35 | 4.1 | 3.2 | – |
| cv | 461 | 29 (6.3) | 10.99 | 13.43 | 41.9 | 36.2 | [ ; ] ∗ |
| Corrected | 608 | 38 (6.2) | 10.09 | 12.15 | 55.3 | 46.8 | [ ; ] ∗ |
| Accepted (% false) | Random draw (T3): false, expected vs BRIDGE | False removed | Gain per update | ||||
|---|---|---|---|---|---|---|---|
| Setting | Decisions | Naive | BRIDGE | Pooled | Within dataset | (%) | BRIDGE / naive |
| (A) | 1,100 | 1,064 (19.1) | 284 (1.1) | 54.2 vs 3 (p ) | 5.5 vs 3 (p 0.15) | 99 [95; 100] | 0.0385 / 0.0156 |
| (B) | 1,400 | 1,323 (20.7) | 475 (1.7) | 98.4 vs 8 (p ) | – | 97 [95; 99] | 0.0329 / 0.0157 |
| (C) | 2,400 | 2,266 (20.0) | 1,199 (0.0) | 239.7 vs 0 (p ) | 0.7 vs 0 (p 0.45) | 100 [100; 100] | 0.0416 / 0.0233 |
| (D) | 3,700 | 3,562 (12.5) | 1,113 (0.5) | 139.0 vs 6 (p ) | 27.4 vs 6 (p ) | 99 [97; 100] | 0.0239 / 0.0115 |
| (E) | 1,280 | 1,236 (25.6) | 192 (1.0) | 49.2 vs 2 (p ) | 12.9 vs 2 (p ) | 99 [98; 100] | 0.0197 / 0.0063 |
| Rule | (A) | (B) | (C) | (D) | (E) |
|---|---|---|---|---|---|
| Accepted updates gaining at most (%) | |||||
| Naive | 38.4 ∗ | 37.3 ∗ | 33.9 ∗ | 39.7 ∗ | 57.4 ∗ |
| McNemar, same POOL | 24.6 ∗ | 53.3 ∗ | 47.1 ∘ | 26.1 ∗ | – |
| McNemar, cross-fit | 22.2 ∘ | 38.0 ∗ | 25.0 ∗ | 14.2 ∗ | – |
| cv paired | 13.7 ∗ | 13.8 ∗ | 8.5 ∗ | 18.1 ∗ | – |
| Corrected resampled | 15.3 ∗ | 14.0 ∗ | 10.2 ∗ | 21.4 ∗ | – |
| Setting | Acc- epted | False | Bound % | LOCO % | Yield /100 | Crit. |
|---|---|---|---|---|---|---|
| (A) weighted | 284 | 3 | 4.23 | 5.95 | 25.82 | |
| (A) balanced accuracy | 848 | 1 | 0.81 | 0.92 | 77.09 | |
| (A) macro- | 829 | 0 | 0.47 | 0.53 | 75.36 | |
| (A) feat. selection + threshold (KNN) | 225 | 1 | 3.45 | 6.00 | 20.45 | |
| (A) feat. selection + threshold (SVC) | 253 | 7 | 7.74 | 11.41 | 23.00 | |
| (D) 26 datasets, 1,000 rows | 558 | 6 | 3.04 | 3.59 | 21.49 |
| (default) | |||||||
|---|---|---|---|---|---|---|---|
| Data | Rule | False % | Bound % | False % | Bound % | False % | Bound % |
| (A) | Naive | 19.08 | 22.90 | 20.44 | 24.23 | 19.46 | 23.16 |
| Same-POOL | 2.65 | 5.85 | 3.61 | 7.02 | 3.80 | 7.17 | |
| BRIDGE | 1.06 | 4.23 | 1.45 | 5.07 | 1.37 | 4.75 | |
| (B) | Naive | 20.71 | 23.52 | 17.36 | 19.93 | 16.88 | 19.43 |
| Same-POOL | 3.18 | 5.14 | 3.62 | 5.48 | 4.84 | 6.84 | |
| Row | Condition | Setting | Evidence | Status |
|---|---|---|---|---|
| 1 | Metrics | (A) | H6 | met |
| 2 | Training sizes | (D) | H6 | met |
| 3 | Multiclass tasks | (D) | H6 | met |
| 4 | Feature selection | (A) | H6 | conditional |
| 5 | Supporting datasets | (D) | H1 | met |
| 6 | OpenML collections | (E), (E2) | H1 , App. G | conditional |
| Minority prev. | Naive: acc. / false (%) | BRIDGE: acc. / false (%) | Bound % | LOCO % | LOCO 0 % | Yield | Crit. |
|---|---|---|---|---|---|---|---|
| weighted- | |||||||
| 20% | 494 / 29 (5.9) | 138 / 1 (0.7) | 5.83 | 11.78 | 6.63 | 27.6 | |
| 10% | 474 / 95 (20.0) | 100 / 0 (0.0) | 4.76 | 14.77 | 14.77 | 20.0 | |
| 5% | 403 / 139 (34.5) | 36 / 0 (0.0) | 16.42 | 48.81 | 48.81 | 7.2 | |
| balanced accuracy | |||||||
| 20% | 500 / 0 (0.0) | 477 / 0 (0.0) | 0.80 | 1.01 | 1.01 | 95.4 | |
| Base learner setting | Acc./ false | % | Cons. % | Yield | Gain | Naive % | Skill | Crit. |
|---|---|---|---|---|---|---|---|---|
| HGB, default (early stop.) | 462/7 | 3.35 | 4.54 | 33.00 | 15.95 | 22.00 | 0.009 | |
| XGBoost, regularized | 893/5 | 1.41 | 1.74 | 63.79 | 61.28 | 9.23 | 0.012 | |
| XGBoost, default (300 rounds) | 146/15 | 17.48 | 23.21 | 10.43 | 1.96 | 31.87 | -0.190 | |
| + early stop. | 963/1 | 0.59 | 1.15 | 68.79 | 71.04 | 6.75 | 0.011 | |
| + min_child_weight 5 | 138/18 | 21.08 | 26.99 | 9.86 | 1.77 | 31.59 | -0.146 | |
| + 31-leaf trees | 125/9 | 14.21 | 21.24 | 8.93 | 1.69 | 32.34 | -0.194 |
| Design | (A) | (B) | (C) | (D) | (E) |
|---|---|---|---|---|---|
| Paper’s design | |||||
| Default (DT, SVC) | 1.1 | 1.7 | 0.0 | 0.5 | 1.0 |
| Members replaced (base HGB) | |||||
| LR and NB | 2.3 | 0.5 | 0.2 | 0.9 | 2.5 |
| MLP and KNN | 1.2 | 1.5 | 0.0 | 1.9 | 4.1 |
| Base learner replaced (members DT, SVC) | |||||
| Base learner | Baseline mean | Final mean | Final minus HGB, points [95% CI] | Better / equal / worse |
|---|---|---|---|---|
| (A) 11 new datasets | ||||
| HGB | 0.855 | 0.864 | +0.000 [+0.000; +0.000] | 0 / 11 / 0 |
| XGB0 | 0.863 | 0.864 | -0.016 [-0.235; +0.210] | 5 / 0 / 6 |
| XGBES | 0.849 | 0.866 | +0.203 [-0.050; +0.521] | 4 / 1 / 6 |
| MLPES | 0.823 | 0.862 | -0.217 [-0.727; +0.367] | 3 / 0 / 8 |
| (D) 39 supporting datasets | ||||
| Learner | Naive acc./ false (%) | BRIDGE acc./ false (%) | Bound % | LOCO % | LOCO 0 % | Yield | Crit. |
| (A) 11 new datasets | |||||||
| HGB | 526 / 97 (18.4) | 86 / 6 (7.0) | 23.86 | 43.42 | 10.49 | 7.8 | |
| DT | 677 / 120 (17.7) | 171 / 6 (3.5) | 10.88 | 20.29 | 5.46 | 15.5 | |
| SVC | 503 / 92 (18.3) | 163 / 6 (3.7) | 11.48 | 24.84 | 6.00 | 14.8 | |
| KNN | 571 / 169 (29.6) | 39 / 4 (10.3) | 49.17 | 59.92 | 33.67 | 3.5 | |
| (B) Synthetic tasks | |||||||
| Per | Net benefit | ||||||
|---|---|---|---|---|---|---|---|
| Task | Acc. | Flagged | TP | FP | Before | After | All |
| BRFSS depression | 197 | 88 291 | 65.3 | 137.8 | 0.0495 | 0.0803 | -0.0116 |
| NHANES diabetes | 200 | 37 390 | 100.3 | 253.4 | 0.0133 | 0.0502 | -0.0467 |
| NHANES asthma | 1 | 0 85 | 22.2 | 62.9 | 0.0000 | 0.0064 | -0.0620 |
| BRFSS asthma | 13 | 1 124 | 31.0 | 92.2 | 0.0002 | 0.0082 | -0.0812 |
| ICU (WiDS) | 180 | 9 112 | 35.8 | 67.3 | 0.0059 | 0.0248 | -0.1421 |