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GoCo: structure-guided conformal calibration for error-controlled Gene Ontology annotation release

Chong Wang, Yongzhao Shao, Peng Liu

arXiv:2610.32990v1q-bio.QMstat.APstat.COstat.MEstat.ML

TL;DR

Computational gene-function prediction produces annotations at a scale that exceeds experimental characterization, while common benchmarks focus on prediction scores rather than error in released annotations. GoCo uses GO-aware risk assessment and predictor-native evidence to construct release policies; across six applications, its structure-specific implementations increased supported yield while keeping mean held-out gene-level FDP at or below target.

  • Problem

    Prediction-score benchmarks such as Fmax and AUPR do not state the error of released annotations, despite computational annotations vastly outnumbering experimentally supported ones.

    Source: §1 · p. 1

  • Method

    GoCo pairs a hierarchy-aware global-threshold certificate with nested release paths built from predictor evidence and certified after ranking policies separately.

    Source: §1 · p. 2, §2.2 · p. 2, §2.3 · p. 3

  • Results

    Across six applications, GoCo increased supported yield while keeping mean held-out gene-level FDP at or below target, with four external applications evaluated without retuning.

    Source: §5 · p. 8

  • Takeaways & Limitations

    GoCo provides a reproducible workflow for comparing annotation release rules, interpreting their error statements, and retaining more reference-supported functions.

    Source: §5 · p. 8

    The guarantee is asymptotic and applies to the fixed panel and reference; GoCo also requires interpretable evidence behind individual calls.

    Source: Limitations and use beyond these… · p. 8

Abstract

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Computational gene-function prediction generates annotations at a scale that experimental characterization cannot match, yet substantial errors remain even among leading methods. Explicit error-controlled calibration for Gene Ontology (GO) prediction remains largely undeveloped. We introduce GoCo, a structure-guided framework that calibrates how scores from an existing predictor are converted into released annotations. GoCo certifies a global threshold for a GO-hierarchy-aware gene-level false discovery proportion (FDP), then constructs a nested release path under the same asymptotic risk-control guarantee. At the primary operating point (alpha=0.10, delta=0.50), GoCo-M, developed on Wainberg co-essentiality modules and applied without retuning to three independent studies with the same shared-evidence structure, kept mean held-out gene-level FDP at or below target while releasing 6.3-17.6% more reference-supported GO terms than Multilabel. For gene-specific neighbourhoods, GoCo-N orders individual calls. Developed on FunMap and validated without retuning on the STRING v12.0 experiments-only network, GoCo-N released 33.8% and 36.4% more reference-supported GO terms than Multilabel on the same refined score grid in FunMap and STRING, respectively, while keeping mean held-out FDP below target. The same pattern held under the stricter delta=0.10 setting. Thus, predictor-native biological structure can be reused at calibration, not only prediction, to release more supported annotations at a chosen gene-level error target without retraining the predictor.

1 Introduction

Computational gene-function prediction produces annotations at scale, but common score benchmarks do not state the error rate of released annotations. GoCo combines GO-aware error assessment with release policies that use predictor-native structure to retain supported annotations at a chosen target.

1 Introduction

  • GoCo addresses the gap between ranking predictions and deciding which annotations to release with a stated gene-level error target.Existing Fmax and AUPR benchmarks summarize predictive performance, not the error of a released set.Source: §1 · p. 1
  • GO’s multiple-inheritance hierarchy and predictor-native gene structure are relevant to release decisions, but a genome-wide cutoff exploits neither.TruePath requires retained ancestors, while shared or gene-specific evidence can distinguish calls that a global score cutoff treats alike.Source: §1 · p. 1
  • GoDag tests whether the average gene-level FDP under a global threshold is within a chosen limit, with a bound on false certification.The release error is the fraction of terms released for a gene that are unsupported by the reference.Source: §1 · p. 2
  • Fixed-size or accuracy-optimized rules lack a gene-level error statement, while a coarse global-threshold path can leave supported calls unreleased.Shared module evidence creates exact score ties that a threshold must admit or exclude as a block.Source: §1 · p. 2
  • GoCo builds structure-specific nested release paths, with GoCo-M for shared evidence and GoCo-N for gene-specific evidence, and establishes asymptotic fixed-sequence control.GoCo-M was developed on Wainberg and evaluated without retuning on Sanger Project Score, Project DRIVE, and HAP1; GoCo-N was developed on FunMap and evaluated on STRING.Source: §1 · p. 2

2 Materials and methods

GoCo leaves predictor scores unchanged, defines reference-based gene-level loss, and separates policy ranking, certification, and evaluation. It constructs nested release paths suited to the predictor’s evidence structure and tests them under a fixed-sequence risk-control procedure.

2.1 Step 1: define the annotation release problem

  • Unsupported calls are those absent from a frozen reference after TruePath closure adds retained ancestors; each gene’s FDP is its loss, and abstention has zero loss.Supported yield is reported separately because FDP does not penalize withheld functions.Source: §2.1 · p. 2

2.2 Step 2: separate ranking, certification and evaluation

  • Across 100 seeded permutations, ranking, certification, and evaluation use 10%, 60%, and 30% of the fixed gene panel, respectively.Certification samples uniformly without replacement from the non-ranking pool, supporting inference without assuming independent gene losses; the guarantee concerns this panel and GO snapshot.Source: §2.2 · pp. 2–3

2.3 Step 3: construct policies from the predictor’s evidence

  • GoDag selects a global threshold using TruePath loss, while GoCo fixes a nested candidate path using ranking labels and frozen inputs before certification.Figure 1 depicts candidate policies being certified in sequence, then evaluates held-out TruePath FDP and reference-supported calls.Source: §2.3 · p. 3, Figure 1 · p. 3

Shared module evidence: GoCo-M.

  • GoCo-M inserts within-grid policies to split shared-score ties, using ranking-fold estimates of unsupported-call probability to order affected genes.Its logistic model uses score, term frequency, and supporting-source reliability; source rates are shrunk toward the ranking-fold average, and identifier hashes resolve ordering ties.Source: Shared module evidence: GoCo-M · pp. 3–4

Gene-specific neighbourhood evidence: GoCo-N.

  • GoCo-N orders individual calls by predicted unsupported probability, creating a separate nested path for gene-specific neighbourhood evidence.It was developed on FunMap and applied without retuning to STRING; the path choice uses evidence structure and score multiplicities, not evaluation outcomes.Source: Gene-specific neighbourhood evidence:… · p. 4

2.4 Step 4: certify the selected release policy

  • Fixed-sequence Learn-Then-Test stops at the first candidate with p_k > δ; its false-certification probability is asymptotically at most δ under stated finite-population conditions.The bound covers any ordering learned from the ranking fold and frozen inputs; δ = 0.50 matches the released Multilabel default, while δ = 0.10 is stricter.Source: §2.4 · p. 4

2.5 Data, comparators and reporting

  • The evaluation covers four module datasets and two neighbourhood datasets, using frozen scores, split streams, and held-out references within each dataset.It reports mean held-out gene-level FDP, supported calls and genes, total calls, and pool-level failure and held-out exceedance frequencies over 100 splits; split variation reflects partitioning of fixed panels, not new populations.Source: §2.5 · pp. 4–5

3 Results

GoCo uses predictor-native structure to release more reference-supported annotations while controlling mean held-out gene-level FDP at the target. Its gains arise across shared-module and gene-specific neighbourhood settings, but path choice is not uniformly best and coverage remains limited.

3.1 Tied scores leave supported annotations unreleased

  • 2,470 Wainberg gene–GO calls tied at score 789.650, and the 800-to-775 threshold step raised full-panel TruePath risk from 0.0924 to 0.1398.GoDag stopped at 800 in all 100 splits; GoCo certified partial admission settings of 35–40% in 89 splits, while the approximately 16% random-admission interpolation was descriptive, not a certificate.Source: §3.1 · p. 5, Figure 2 · p. 6

3.2 Shared module evidence: GoCo-M

  • 8.7%, 14.3%, 17.6% and 6.3% more supported yield than Multilabel was achieved by GoCo-M in Wainberg, Sanger, DRIVE and HAP1, respectively.Mean held-out FDPs were 0.0964, 0.0980, 0.0971 and 0.0943; gains persisted at δ = 0.10.Source: §3.2 · p. 5

3.3 Confidence and error-target sensitivity

  • At δ = 0.50, GoCo-M exceeded the pool-risk target in 5–26% of splits, while mean held-out FDP remained below target at α = 0.05 and 0.20 for the principal methods.At α = 0.20, δ = 0.50, DRIVE showed zero gain because both methods reached the grid’s reporting floor.Source: §3.3 · p. 5

3.4 Yield and biological interpretation

  • In Wainberg split 0, 37 of 351 added calls were reference-supported; 27 of 35 interleukin-6 signalling calls for IL6ST and JAK1 were supported, while none of seven transferred TP53 terms was.Only about 8–12% of held-out genes received calls; the gene-averaged target controls neither FDP among annotated genes alone nor the pooled fraction of unsupported calls.Source: §3.4 · p. 5

3.5 Gene-specific neighbourhood evidence: GoCo-N

  • 33.8% and 36.4% more supported calls than Multilabel were released by GoCo-N on the same refined score grid in FunMap and STRING, respectively.Mean held-out FDP was 0.0921 and 0.0944; the stricter δ = 0.10 gains were 34.0% and 35.4%.Source: §3.5 · p. 5

3.6 Comparison with accuracy-based release rules

  • Validation Fmax thresholds and one top-scoring term per gene exceeded 0.10 gene-level FDP in every split of every predictor, despite recovering more supported functions by releasing more calls.These accuracy-based rules provide no way to certify the accompanying gene-level error rate.Source: §3.6 · p. 6

4 Discussion

GoCo uses evidence behind calls to improve supported yield while allowing release policies to be compared without retraining the predictor. Its gene-averaged FDP and guarantee have defined scope and limitations.

4 Discussion

  • GoCo uses evidence behind calls to improve supported yield, and its protocol separates policy ordering from certification so release rules can be compared without retraining.The module-structure comparison covers Wainberg and three external studies with shared-evidence structure; the neighbourhood comparison covers FunMap and external STRING validation.Source: §4 · p. 6, Table 1 · p. 7, Table 2 · p. 7
  • Gene-averaged FDP is not pooled call-level FDR or a guarantee for each gene or subgroup.Reference-supported yield and reference-based FDP should be interpreted together because GO is incomplete and functional relevance varies across biological contexts.Source: §4 · p. 6

Limitations and use beyond these predictors

  • The asymptotic guarantee requires nonvanishing variance at the first invalid candidate and applies to the fixed panel and reference.The primary δ = 0.50 setting is a benchmark convention, and the better path cannot yet be predicted reliably from structure alone.Source: Limitations and use beyond these… · p. 8
  • GoCo additionally requires interpretable evidence behind individual calls; proposed shared and gene-specific evidence sources require empirical validation.GoDag needs only scores; possible extensions include protein complexes, co-regulation clusters, homology hits, embedding neighbours, and integrated networks.Source: Limitations and use beyond these… · p. 8

5 Conclusions

GoCo combines an unchanged predictor with GO-aware error assessment and structure-guided release policies. Across six applications, its implementations increased supported yield while keeping mean held-out gene-level FDP at or below target.

5 Conclusions

  • Across six applications, structure-specific GoCo implementations increased supported yield while keeping mean held-out gene-level FDP at or below target.Four external applications were evaluated without retuning.Source: §5 · p. 8
  • GoCo provides a reproducible workflow for comparing annotation release rules, interpreting their error statements, and retaining more reference-supported functions.Source: §5 · p. 8

Key Points

GoCo combines GO-aware calibration with evidence already exposed by an unchanged predictor. Its structure-specific implementations increase supported yield under gene-level FDP control, with the guarantee limited to pool-average gene-level risk.

Key Points

  • Accuracy-optimized and fixed-size release rules provide no gene-level error certificate; FDP ranged from 0.17 to 0.99 across these applications.Source: Key Points · p. 8
  • GoCo combines GO-aware calibration with evidence already exposed by an unchanged predictor.Source: Key Points · p. 8
  • The asymptotic certificate controls pool-average gene-level FDP, not pooled-call FDR or each gene’s error.Source: Key Points · p. 8
  • GoCo-M increased supported yield by 6.3–17.6% over Multilabel across four module datasets at the primary operating point.Figure 4 plots mean held-out gene-level TruePath FDP against the target and supported-call gain relative to Multilabel across α = 0.05, 0.10, and 0.20.Source: Key Points · p. 8, Figure 4 · p. 9
  • GoCo-N increased supported yield by 33.8% and 36.4% in FunMap and STRING against Multilabel on the same refined score grid.Source: Key Points · p. 9

Funding

This work was supported by the Plant Sciences Institute and the Laurence H. Baker Center for Bioinformatics and Biological Statistics at Iowa State University.

Funding

  • This work was supported by the Plant Sciences Institute, Iowa State University; and the Laurence H. Baker Center for Bioinformatics and Biological Statistics, Iowa State University.Source: Funding · p. 9

Data availability

The study generated no new experimental data and makes its implementation and reproducibility materials available.

Data availability

  • No new experimental data were generated in this study.Source: Data availability · p. 10
  • The repository provides reference implementations, tests, scripts, fold assignments, analysis outputs, and aggregate summaries.Source: Data availability · p. 10
  • The software and reproducibility materials are archived on Zenodo under concept DOI 10.5281/zenodo.22677009.Source: Data availability · p. 10

Author descriptions

The author descriptions outline research roles and areas spanning statistics, biostatistics, epidemiology, and bioinformatics.

Author descriptions

  • Chong Wang is a professor at Iowa State University whose research includes biostatistics, epidemiology, diagnostic test evaluation, network meta-analysis, and bioinformatics.Source: Author descriptions · p. 10
  • Yongzhao Shao is a professor at NYU Grossman School of Medicine whose research spans biostatistics for precision medicine, epidemiology, survival analysis, and gene–environment interaction.Source: Author descriptions · p. 10
  • Peng Liu is a professor at Iowa State University and directs its bioinformatics and biological statistics center, with research in statistical genomics and high-dimensional inference.Source: Author descriptions · p. 10

Supplementary material for: GoCo: structure-guided conformal calibration for error-controlled Gene Ontology

The supplement collects proofs, construction details, implementation material, and additional analyses for GoCo and its baseline.

Supplementary material

Supplementary Note S1: Proofs

Supplementary Note S1 establishes the sampling and asymptotic arguments behind GoCo’s risk guarantee, then explains how candidate-path structure and ordering affect risk and release decisions.

S1.1 Setting and notation

  • The fixed gene panel, scores, GO snapshot, and references make each policy’s gene loss fixed; a random permutation assigns ranking, certification, and evaluation folds.The folds contain approximately 10%, 60%, and 30% of the panel, respectively.Source: S1.1 Setting and notation · p. 13

S1.2 The split as a sampling design

  • Conditional on the ranking fold, certification is simple random sampling without replacement from the pool, supporting unbiased sample means and finite-population variance calculations.Source: S1.2 The split as a sampling design · p. 13

S1.3 Finite-population central limit theorem

S1.4 Structure of the candidate path

  • GoCo’s candidate release sets are nested and the path is determined by the ranking fold, but nestedness does not imply monotone losses.Path construction decisions use ranking-fold labels and frozen predictor objects; only call counts are guaranteed to be monotone.Source: S1.4 Structure of the candidate path · p. 14

S1.5 Consistency of the variance estimator

  • The certification-fold variance estimate converges to the pool variance in probability as the certification sample grows, and its standard deviation is ratio-consistent when variance stays positive.Source: S1.5 Consistency of the variance… · p. 14

S1.6 Proof of main-text Proposition 1

  • The fixed-sequence rule’s selected policy has asymptotic risk-exceedance probability bounded by Φ(zδ/√(1−f)) under the stated conditions, with the bound at most δ for δ ≤ 0.50.The argument applies to any ranking-fold-measurable ordering when the variance condition holds uniformly; path length does not enter the asymptotic error term.Source: S1.6 Proof of main-text Proposition 1 · p. 15

S1.7 Proof of Remark S2

  • At δ = 0.50, held-out exceedance bounds pool-level failure from above, but a held-out exceedance does not establish that pool risk exceeded target.The stopping rule can select a certification mean slightly below target, producing held-out exceedances even when pool risk is near target.Source: S1.7 Proof of Remark S2 · p. 16

S1.8 Proof of Lemma S6

  • Partial admission can gain granularity over a global threshold, while ordering’s average risk saving is positive when later-admitted genes have larger increments.These properties do not guarantee a larger certified prefix or optimal yield; whether the learned ordering is favorable on pool genes is empirical.Source: S1.8 Proof of Lemma S6 · p. 16

Supplementary Note S2: Construction and implementation details

Supplementary Note S2 describes GoCo’s split, ranking, certification, and implementation procedures, including its gene-averaged risk target against a frozen TruePath reference and structure-guided annotation release. It also covers FunMap and STRING validation, construction choices, differences among structural paths and their matched-risk performance across datasets, and the rationale for selecting candidate paths.

S2.1 Splits: seeds, rounding and realised fold sizes

  • Across 100 random streams, GoCo uses ranking, certification, and evaluation folds of about 10%, 60%, and 30%, respectively, and evaluates unsupported calls against the frozen TruePath reference.Reference-unsupported is an operational label after TruePath closure, not a claim that a function is biologically absent; evaluation labels are withheld until evaluation.Source: S2.1 Splits: seeds, rounding and… · p. 18, S2.2 Interpretation of the frozen… · p. 18

S2.3 The per-call ranking model

  • GoCo estimates unsupported-call probabilities from shared-source evidence and predictor features, then ranks genes by predicted loss increment per predicted supported term.The module model uses seven per-call features, including shrunk source and term unsupported rates; label-derived features use ranking-fold labels, and the ordering affects yield rather than validity.Source: S2.3 The per-call ranking model · p. 18, S2.7 Further conventions and definitions · p. 20

S2.4 Remark S2: the split identity and held-out exceedance

  • Held-out exceedance of α at δ = 0.50 occurred in 19–42% of GoCo splits across four datasets, consistent with evaluation-fold risk overshooting the pool risk.The pool risk is computable here and directly checks Proposition 1; GoDag’s Wainberg calibration mean was approximately 0.092, with 1% exceedance, while external GoDag exceedance was 36% and 28% in Sanger and DRIVE. The predictor’s reporting floor bound all methods in DRIVE at α = 0.20, δ = 0.50, and one Sanger split under that setting.Source: S2.4 Remark S2: the split identity and… · p. 19, S2.7 Further conventions and definitions · p. 21

S2.5 The uniform grid path and the choice of ranking statistic

  • GoCo uses a uniform candidate grid with partial admissions at ranking-fold triggers and orders candidates by predicted loss per predicted supported term, a cost-per-gain heuristic.The path accommodates thresholds after inserted policies but does not guarantee a larger certified prefix.Source: S2.5 The uniform grid path and the… · p. 19

S2.6 A worked micro-example of one block

  • In the Wainberg 800-to-775 step, 2,470 of 2,484 gene–GO rows shared one score, while GoCo certified admission of 35% or 40% of affected genes in 89 of 100 splits.The full-panel interpolation reaches α at about q = 0.16, but this is not a certification calculation; split 0 admitted 40%.Source: S2.6 A worked micro-example of one block · p. 19

S2.7 Further conventions and definitions

  • The certified risk averages per-gene FDP across pool genes, assigns abstentions zero loss, and neither controls pooled call-level FDR nor constrains each annotated gene.The proposition is asymptotic in certification size and controls pool risk, not the noisy evaluation-fold mean; δ = 0.50 reduces the normal certificate to an empirical calibration check.Source: S2.7 Further conventions and definitions · pp. 19–20

S2.8 Source objects beyond co-essentiality

  • GoCo applies to predictors exposing frozen scores and call-specific evidence objects, provided the focal gene is excluded; FunMap uses proximity-weighted source evidence and individual-call ordering.The FunMap wrapper removes each focal gene from its neighbourhood and enrichment background, and the implementation was applied without retraining; its GO release was frozen at 2024-09-08.Source: S2.8 Source objects beyond… · p. 21, S3.1 FunMap: the predictor and the… · p. 23

S2.9 Gene-level case study of the released annotations

  • In Wainberg split 0, GoCo-M admitted 40% of affected genes and added 351 evaluation-fold calls across 158 genes, of which 37 (10.5%) were reference-supported.Examples include supported transfers within the IL6ST/JAK1/LIFR/SLC39A1/STAT3 module and unsupported transfers of transcription-factor functions to CDKN1A; reference-unsupported calls are not necessarily biologically false.Source: S2.9 Gene-level case study of the… · p. 21

S3.2 STRING: validation without retuning, and why this network and not another

  • STRING experiments-only edges provide a GO-independent validation network, with GO-linked columns excluded and GO-trained alternatives rejected as circular.STRING was frozen before FunMap’s publication and uses physical-assay evidence; the experiments channel uses column 10 only, and its score floor means pairs with experiments scores above 150 were not censored on GO-derived grounds.Source: S3.2 STRING: validation without… · pp. 23–24

S3.3 Why the structure differs, and what Lemma S6 implies

  • Exact Wainberg score ties block global-threshold granularity, whereas tie-light FunMap and STRING benefit from grid refinement and GoCo-N adds a prespecified call ordering.Lemma S6 separates granularity from ordering; GoCo-N ranks individual calls by bpig on a fixed geometric grid, with ties broken by frozen gene hash and call index. This is a candidate-path heuristic, not an optimality result; GoCo-M instead ranks genes within blocks by predicted loss increment per predicted supported term.Source: S3.3 Why the structure differs, and… · p. 24

S3.4 What the comparison shows

  • Grid refinement raised supported-call yield approximately 5.0% at α = 0.10, δ = 0.50 and 1.5% at δ = 0.10; GoCo-M gained supported calls over the matched-risk frontier in both networks.At δ = 0.10, GoCo-M gained +101, +196 and +164 calls in FunMap and +46, +138 and +197 in STRING at α = 0.05, 0.10 and 0.20, respectively, and was ahead in 100% of splits at each setting.Source: S3.4 What the comparison shows · p. 24
  • GoCo-N gained +155, +379 and +519 supported calls in FunMap and +172, +268 and +561 in STRING against the matched-risk frontier at δ=0.10.It was ahead in 95%, 100% and 100% of FunMap splits and 100%, 97% and 99% of STRING splits; at α = 0.10 it covered 1,084 annotated genes in FunMap versus 779 for GoCo-M.Source: S3.4 What the comparison shows · p. 24

S3.5 Both instantiations on the four dependency data sets

  • At α = 0.10, δ = 0.10, GoCo-N released 142 fewer reference-supported terms than GoCo-M in Wainberg and 69 fewer in DRIVE, but 219 more in Sanger and 88 more in HAP1.The per-call model and cross-fitting were unchanged, so only the candidate path differed; this variation motivated a ranking-fold rule to choose between paths before certification without evaluation-fold outcomes.Source: S3.5 Both instantiations on the four… · p. 25

S3.6 An adaptive alternative to the structural mapping

The supplement describes a ranking-fold adaptive choice between GoCo-M and GoCo-N, alongside candidate-path construction and certification details. It also reports measurability checks and module-family data reconstruction.

S3.6 An adaptive alternative to the structural mapping

  • The rule walks both instantiations on ranking-fold data and carries forward the path with higher supported-call yield; predicting the winner from structure alone remains open.The adaptive choice uses ranking-fold labels, whereas the prespecified structural mapping requires no per-dataset decision and is immediately applicable to a new predictor.Source: S3.6 An adaptive alternative to the… · p. 25
  • At α = 0.10 and δ = 0.10, T-selected GoCo released 6.0–73.4% more supported terms than the cutoff across six predictors.It agreed with the held-out winner in 100%, 96%, 80%, 89%, 83% and 69% of splits across Wainberg, Sanger, DRIVE, HAP1, FunMap and STRING, respectively.Source: S3.6 An adaptive alternative to the… · p. 25

S3.7 Measurability

  • Scrambling labels outside the ranking fold left per-call ordering unchanged across 241,154 FunMap and 470,735 STRING calls, but cannot detect labels carried by frozen predictor columns.The authors exclude the background count by inspection rather than by the scrambling test.Source: S3.7 Measurability · p. 25

S4.1 Candidate construction

  • GoCo-M estimates unsupported-call probabilities from ranking-fold labels and frozen outputs, then uses predicted loss increase per supported term to order affected genes and refine the nested path.The insertion triggers use ranking-fold data only, and the construction is identical across datasets.Source: S4.1 Candidate construction · p. 26

S4.2 Certification rule and formal guarantees

  • Fixed-sequence testing checks candidate policies in path order and returns the candidate before the first p-value exceeding δ; replacing the normal test with Hoeffding gives finite-sample control.The paper states that validity does not depend on the T-measurable ordering: predictor-native evidence changes which policies are reached before failure, not the error bound.Source: S4.2 Certification rule and formal… · pp. 26–27
  • Random partial admission interpolates risk linearly between global endpoints, while ordering genes by smaller risk increments can lower risk at intermediate admissions.The average risk saving relative to random admission equals N^-1 times the covariance between rank and risk increment; a nondecreasing increment-by-rank order is optimal at every admission count.Source: S4.2 Certification rule and formal… · p. 27

S4.3 Module reconstruction and frozen reference

  • The Wainberg reconstruction reproduces archived scores to numerical precision and names the source members for each call; comparisons use shared split streams, scores and held-out truth.Sanger Project Score and Project DRIVE use the same Wainberg modules with different dependency evidence, while HAP1 uses published genetic-interaction clusters.Source: S4.3 Module reconstruction and frozen… · p. 27
  • Table S1 compares operating characteristics for five release methods at α = 0.10 across two δ settings and 100 splits.Its descriptions distinguish the TruePath and Direct losses, candidate paths, calibration samples, and supported-call measures.Source: Table S1 · p. 28, S4.3 Module reconstruction and frozen… · p. 28
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