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BFHD: Bidirectional Feature Harmonization Decomposition for Heterogeneous Clinical Assessments

Yuanhao Zhuo, Zixi Qin, Ling Qin, Wanqing Li

arXiv:2610.19352v1cs.LG

TL;DR

Heterogeneous assessment systems leave clinical records mixing related but distinct measurements, while score-level linking does not identify which individual measurements translate reliably both ways. BFHD uses coupled translation and feature-wise gating to decompose measurements by bidirectional recoverability. It achieves the best overall structure recovery accuracy and strong subset stability across seeds among bidirectional baselines.

  • Problem

    Heterogeneous clinical assessment systems complicate integration, and total-score linking does not identify which individual measurements are recoverable in both directions.

    Source: §1 · p. 1

  • Method

    BFHD couples translations between paired assessment systems and uses feature-wise gating to identify recoverable subsets and separate non-translatable measurements.

    Source: §1 · p. 2, §3 · p. 2, §3.1 · p. 2

  • Results

    BFHD achieves the best overall structure recovery accuracy and strong subset stability across seeds among bidirectional baselines.

    Source: Results · p. 5

  • Takeaways & Limitations

    BFHD's identified structure supports cross-protocol integration, temporal deployment under protocol drift, and robustness to test-time missingness.

    Source: §1 · p. 2

    When multiple maximal feasible solutions exist, BFHD recovers one, and stability across random initializations is used to assess identifiability.

    Source: §3.4 · p. 3

Abstract

from arXiv · show

Clinical assessments are often collected using heterogeneous assessment systems across centers and time, leading to records that mix different but related sets of measurements. This motivates harmonization beyond total-score linking. We formulate clinical harmonization at the measurement level as a bidirectional recoverability problem: given paired observations from two assessment systems, the goal is to identify which measurements can be reliably translated in both directions within an application-defined tolerance, while separating non-translatable components. We propose Bidirectional Feature Harmonization Decomposition (BFHD), a feasibility-driven framework that enforces bidirectionally coupled translation and uses feature-wise output gating to produce an explicit decomposition in the original measurement space. Experiments on synthetic data and real clinical assessment pairs show that BFHD achieves broader feasible harmonization coverage and improved subset stability compared to baselines.

1 Introduction

Clinical records combine different assessment systems, but total-score linking does not reveal which individual measurements translate reliably in both directions. BFHD frames harmonization as measurement-level recoverability and decomposes measurements into recoverable and non-translatable components.

1 Introduction

  • Different centers, cohorts, and time periods use different assessment systems, producing longitudinal records that mix related but distinct measurements.This heterogeneity complicates clinical data integration and longitudinal analysis.Source: §1 · p. 1
  • Existing total-score linking and calibration methods do not identify which individual measurements are bidirectionally recoverable across heterogeneous assessments.This leaves clinicians and researchers without guidance on which measurements can be harmonized and which should remain system-specific.Source: §1 · p. 1
  • BFHD identifies measurements that translate bidirectionally and separates them from non-translatable components in the original measurement spaces.Its coupled translation model and feature-wise gating enforce cross-system feasibility within a clinically meaningful tolerance, without task supervision or latent projections.Source: §1 · pp. 1–2
  • On synthetic and real clinical datasets, BFHD reveals meaningful harmonization structure and supports cross-protocol integration, temporal deployment under protocol drift, and test-time missingness robustness.The framework is presented as a feasibility-driven approach to identifying large bidirectionally recoverable subsets.Source: §1 · p. 2

2 Related Work

Prior approaches address harmonization through score-level linking, prediction, latent representations, or feature selection, but they do not directly identify bidirectionally recoverable observed measurements. BFHD instead targets explicit recoverability in the original measurement space.

2.1 Clinical Harmonization and Task-Driven Baselines

  • Score-level linking and calibration align outcomes, while predictive mappings and ComBat-style harmonization do not characterize intrinsic bidirectional recoverability or preserve system-specific content.Predictive feature attributions depend on the chosen target, whereas ComBat-style methods remove site or batch effects as nuisance variation.Source: §2.1 · p. 2

2.2 Multiview Learning and Bidirectional Structure

  • Multiview methods capture cross-view dependence in latent spaces, while cycle-consistent and tied-weight models couple directions without explicit subset selection.BFHD's strict shared-constraint coupling is instantiated with invertible networks, with a tied-weight MLP as a non-invertible alternative.Source: §2.2 · p. 2

2.3 Gating and Its Relation to Feature Selection

  • Unlike task-driven feature selection, BFHD gates represent membership in a bidirectionally recoverable subset under feasibility-style reconstruction constraints.This yields an explicit decomposition into recoverable and non-translatable components aligned with clinical harmonization.Source: §2.3 · p. 2

3 Problem Formulation

BFHD frames measurement-level harmonization as finding the largest subsets of paired assessment features that are recoverable in both directions within an application-defined tolerance. Its feasibility is model-relative, approximate, and potentially non-unique.

3.1 Bidirectional model class

  • The two mappings must be coupled so learning in either direction constrains the mapping in the other direction.Source: §3.1 · pp. 2–3
  • ε-recoverability means a feature's population-level reconstruction error is below an application-level tolerance for clinically acceptable agreement.Source: §3.1 · p. 3
  • The population conditions and combinatorial subset search are relaxed using continuous feature gates, which stay open when the shared operator reconstructs features with sufficiently small empirical error.Source: §3.1 · p. 3
  • The recoverable subsets depend on the chosen bidirectional model class and tolerance: looser ε admits broader translation, while stricter ε imposes tighter harmonization.Source: §3.1 · p. 3

3.3 Feasible decompositions

  • An ε-feasible decomposition permits selected features to satisfy approximate rather than exact reconstruction, accommodating realistic clinical noise.Source: §3.3 · p. 3

3.4 The BFHD optimization problem

  • BFHD seeks the largest bidirectionally recoverable subsets of paired assessment measurements, treating their complements as non-translatable.Source: §3 · p. 2, §3.4 · p. 3
  • The optimization maximizes a user-weighted sum of the recoverable subset sizes across the two systems.Source: §3.4 · p. 3
  • When several maximal feasible solutions exist, BFHD returns one, and stability across random initializations is used to assess identifiability.Source: §3.4 · p. 3

4 Methodology

BFHD implements measurement-level harmonization with a shared bidirectional mapping, feature-wise output gates, and cross-view reconstruction losses. The objective rewards broad recoverable subsets while closing gates for features that fail feasibility constraints.

4 Methodology

  • The methodology combines a shared bidirectional backbone, feature-wise gates, and cross-view reconstruction losses to approximate recoverable subsets and enforce feasibility.Source: §4 · p. 3

4.1 Architecture Overview

  • The same backbone maps X to Y and Y to X, with output gates selecting which measurements must be reconstructed and contribute to loss.Source: §4.1 · p. 3

4.2 Bidirectional Backbone via Invertible Networks

  • A NICE-style invertible network supplies one operator and its analytic inverse for strict parameter sharing; zero-padding aligns dimensions without supervising padded features.Source: §4.2 · p. 4

4.3 Output L0 Gating

  • Output gates near one mark features as recoverable and gates near zero as non-translatable, while full inputs remain available to the mappings.Source: §4.3 · p. 4

4.4 Gated Hinge Losses

  • Gated hinge losses use feature-wise normalized squared error and a stricter training tolerance; ordinal items are treated as numerical scores.Source: §4.4 · p. 4

4.5 Gate Reward Term

  • A gate reward favors inclusion, while reconstruction losses counter it by closing gates for features with poor bidirectional reconstruction.Source: §4.5 · p. 4

4.6 Overall Objective

  • The total objective jointly trains the shared operator and gates, with staged training used to stabilize optimization and avoid degenerate solutions.Source: §4.6 · p. 5

5 Experiments

The experiments evaluate synthetic measurement-level structure recovery, real-world harmonization coverage, temporal retention under protocol drift, and component ablations. Across these settings, BFHD recovers broader feasible subsets with stability advantages over baselines.

5.1 Experimental Setup

  • The setup uses synthetic data with ground-truth labels and paired clinical assessments, evaluates 10 random seeds, and reports structure-recovery accuracy and subset Jaccard stability.Real-world recoverability is evaluated using εcutoff = 0.6; synthetic baselines without gates use a relaxed 2εgen criterion.Source: §5.1 · p. 5, Evaluation protocol · p. 5

Results.

  • BFHD achieves the best overall synthetic structure-recovery accuracy with strong subset stability among bidirectional baselines.Methods without feasibility-driven gating show greater seed variability on weakly recoverable measurements near the 2εgen boundary.Source: Results · p. 5, Table 1 · p. 5

5.3 Experiment 2: Real-World Harmonization

  • The real-world experiment targets harmonization coverage and stability rather than maximizing reconstruction accuracy because measurement-level equivalence lacks definitive ground truth.The reported primary metric is the number of recoverable measurements, with Jaccard similarity assessing seed stability.Source: §5.3 · p. 6
  • Across a broad ε range, BFHD recovers more measurements than baselines; its advantage is especially pronounced around εcutoff ∈ [0.55, 0.8], where baseline coverage can be conservative or unstable.The ε-sweep figure plots median #rec against ε for EMBIC↔NeuroBAT.Source: §5.3 · p. 6, Figure 1 · p. 6
  • BFHD identifies larger recoverable subsets across real-world settings while maintaining comparable or improved seed stability, and matches baselines on strongly aligned measurements while increasing marginally aligned measurements.The real-world comparison uses εcutoff = 0.6; Table 2 reports recoverable counts, Jaccard stability, and CCC-based diagnostics.Source: §5.3 · p. 6, Table 2 · p. 7

5.4 Experiment 3: Temporal Deployment Utility under Protocol Drift

  • Under temporal shift on EMBIC↔NeuroBAT, BFHD retains more training-period recoverable measurements and achieves higher retention rates than baseline approaches.Retained measurements must remain feasible on the held-out later cohort.Source: §5.4 · pp. 6–7, Table 3 · p. 7

5.5 Experiment 4: Ablation and Stability Analysis

  • Ablations show that replacing the L0 gate reward with a standard penalty yields degenerate solutions, while removing output gating reduces subset stability.A tied-weight non-invertible MLP preserves subset size, suggesting invertibility is not required for feasibility-based coverage.Source: §5.5 · p. 7, Table 4 · p. 7

6 Conclusion

The conclusion presents BFHD as a feasibility-driven decomposition that identifies bidirectionally recoverable measurement subsets and reports broader coverage and higher stability across synthetic and clinical assessment pairs. The accompanying implementation uses a shared bidirectional backbone, output gates, and staged training.

6 Conclusion

  • Across synthetic data and real clinical assessment pairs, BFHD yields broader feasible harmonization coverage and higher subset stability than baselines, providing an explicit decomposition for cross-protocol integration.The framework identifies bidirectionally recoverable subsets under a shared operator.Source: §6 · pp. 7–8

A.1 Backbone Architecture

  • BFHD uses a NICE-style invertible network with additive coupling layers to enforce strict parameter sharing across directions, not for likelihood modeling.The selected architecture is shared across datasets; feasibility-related hyperparameters are tuned per dataset.Source: §A.1 · p. 8

A.2 Training Procedure

  • Training proceeds through backbone warm-up, joint optimization with feasibility constraints, then gate hardening and backbone fine-tuning.During joint optimization, the gate reward and hinge-style feasibility loss are used together; the training tolerance is annealed.Source: §A.2 · p. 8

A.3 Hard-concrete L0 output gates

  • Learnable hard-concrete gates produce continuous values during training and are binarized after convergence; a measurement is recoverable when its hardened gate is active.The gates use an L0 relaxation.Source: §A.3 · p. 8

A.4 Optimization and Learning Rates

  • Gated models use separate learning rates for backbone and gate parameters, while neural models use Adam and validation-based early stopping.A single learning rate can cause unstable gating or degraded backbone mappings.Source: §A.4 · p. 8

A.5 Hyperparameter Selection

  • The backbone configuration is selected by greedy search and then fixed across datasets, while feasibility-related hyperparameters are tuned per dataset.The training tolerance is set to εtrain = 1/6 εcutoff.Source: §A.5 · p. 8

A.6 Baseline Implementations

The appendix specifies baseline implementations, a measurement-anchored protocol for setting feasibility tolerance, synthetic data construction, and the clinical assessment datasets used in the experiments.

A.6 Baseline Implementations

  • FRF and XGBoost are tuned over specified estimator and model-parameter grids, while CMLP uses a four-layer network and TWMLP replaces the invertible backbone with a shared MLP.TWMLP retains BFHD’s gating, feasibility losses, annealed εtrain, and learning-rate separation to isolate the effect of invertibility.Source: §A.6 · p. 8

A.7 Protocol for Setting the Feasibility Tolerance εcutoff

  • The protocol anchors εcutoff to measurement variability, converts SEM to NMSE-scale tolerance when same-metric SD is available, takes the largest subtest tolerance as the system threshold, and sets SNAP-IV εcutoff to 0.6.εcutoff is a reference threshold users may adjust within a reasonable range; it is not universal.Source: §A.7 · p. 9

B.1 Synthetic Data Generation

  • Synthetic paired observations separate shared factors from system-specific private factors, with features labeled recoverable only when they depend exclusively on shared factors.Recoverable features include redundant groups and attenuated, weakly recoverable features near the ε-recoverability boundary.Source: §B.1 · p. 9, Latent Variables · p. 9, Feature Partition and Ground-Truth… · p. 9
  • The synthetic generator adds independent feature noise and probabilistic nonlinear folding, preserving shared dependence while introducing information loss and breaking strict invertibility.Its specified Exp. 1 setting uses 2,000 observations, 20 features per system, and nonlinear folding with probability 0.95.Source: Measurement Noise · p. 10, Nonlinear Folding · p. 10, Synthetic parameterization (Exp. 1) · p. 10
  • The generator records ground-truth recoverability and distortion indices, enabling controlled evaluation of feature-level recovery and subset stability under redundancy, weak shared structure, noise, and folding.Exp. 1 uses 10 recoverable features per view, with three redundancy groups per view and 35% weak-shared recoverables.Source: Synthetic parameterization (Exp. 1) · p. 10, Summary · p. 10

B.2 ADNI Cognitive Assessments (EMBIC and NeuroBAT)

  • ADNI pairs EMBIC’s 13 numerical measurements with NeuroBAT’s 9 measurements, retaining each subject’s earliest assessments within a 28-day window and 1,629 complete paired observations.The assessment representations use test means for EMBIC and individual item or subtest total scores for NeuroBAT; missing cases are removed without imputation.Source: §B.2 · p. 10

B.3 ADHD Assessments (CAS and SNAP-IV)

  • The ADHD dataset pairs 27 CAS measurements with 18 SNAP-IV measurements, using earliest assessments within a 28-day window and retaining 336 complete paired observations.SNAP-IV includes Inattention and Hyperactivity/Impulsivity subscales; CAS includes normatively converted subscales, subtest totals, and the overall total score.Source: §B.3 · pp. 10–11
  • The ADHD dataset is available upon reasonable request, subject to the relevant data use agreement.Source: §B.3 · p. 11

B.4 Data Splitting Protocol

The datasets use a 7:1:2 training, validation, and test split; Experiment 3 uses date-ordered splits to evaluate temporal shift, and the additional utility analyses use CAS and SNAP.

B.4 Data Splitting Protocol

  • All datasets are split 7:1:2 for training, validation, and testing.Source: §B.4 · p. 11

C Additional Utility Analyses

C.1 Experiment 5: Downstream Prediction under Size-Matched Harmonized Subsets

In downstream prediction, translated measurements have lower accuracy than observed measurements, but BFHD performs best among the compared harmonization methods. Under test-time missingness, retention declines as missingness rises, with BFHD competitive or stronger than baselines.

C.1 Experiment 5: Downstream Prediction under Size-Matched Harmonized Subsets

  • The downstream task uses CAS ↔ SNAP because it has an external label, with translation into a fixed prediction space when only the opposite assessment is available at deployment.Methods are compared using subsets matched to the median BFHD recoverable-subset size, with baseline measurements ranked by validation NMSE.Source: §C.1 · p. 11
  • The study trains identical linear SVM classifiers across methods and seeds and compares observed and translated subset representations with full single-view references.Translated measurements for classifier training are generated using a held-out validation split to reduce optimistic bias.Source: §C.1 · p. 11

Results

  • Translated measurements yield lower accuracy than observed measurements in both deployment settings, but BFHD has the highest mean translated-measurement accuracy and smallest degradation among harmonization methods.Source: Results · p. 12, Table 5 · p. 12

Experimental setup

  • Missingness is introduced only at inference after training on fully observed pairs, using MCAR entry dropping and mean imputation in standardized space in either deployment direction.Source: §C.2 · p. 12, Experimental setup · p. 12

Evaluation protocol

  • Retention measures the fraction of measurements feasible in the clean evaluation that remain feasible under missingness, reported across random seeds.Source: Evaluation protocol · p. 12

Results and discussion

  • Retention falls monotonically as missingness rises; BFHD retains more feasible measurements than CMLP at 10% missingness and is comparable or better than baselines at higher rates, with trends consistent across directions.At 10% missingness, BFHD is competitive with NICE and has lower variability across seeds.Source: Results and discussion · p. 12

D.1 Additional Results for Experiment 1: Synthetic Experiments

Across synthetic data-generation seeds, BFHD achieves consistently strong recoverability accuracy and subset stability; Jaccard similarity better reflects stability than accuracy variance.

D.1 Additional Results for Experiment 1: Synthetic Experiments

  • CCC is a diagnostic of agreement strength, not an optimization target; moderate CCC is expected for measurements near the feasibility boundary.Source: §D.1 · pp. 12–13
  • BFHD achieves consistently strong index-level recoverability accuracy and subset stability across synthetic data-generation seeds, with Jaccard similarity better reflecting stability than accuracy variance.Source: §D.1 · p. 12, Table 7 · p. 13

D.2 Additional Results for Experiment 2: Real-World Harmonization

Across real-world assessment pairs, BFHD shows broader feasible measurement coverage and strong or comparable retained-measurement agreement under temporal protocol drift. On CAS↔SNAP, its coverage advantage is especially pronounced at intermediate feasibility thresholds.

D.2 Additional Results for Experiment 2: Real-World Harmonization

  • Across thresholds, BFHD identifies more feasible measurements than baselines in both CAS and SNAP, with the largest advantage at intermediate ε.The ε-sweep reports median recoverable-measurement counts separately for CAS and SNAP, aggregated over random seeds.Source: §D.2 · p. 13, Figure 2 · p. 14
  • The CAS↔SNAP sweep is consistent with the main paper’s reference-threshold Jaccard stability finding: BFHD expands feasible coverage under a shared feasibility criterion.Source: §D.2 · p. 13

D.3 Additional Results for Experiment 3:

  • Across both real-world pairs and deployment directions, BFHD retains a larger fraction of training-period recoverable measurements on later cohorts while maintaining strong or comparable CCC agreement among retained measurements.For EMBIC→NeuroBAT, several baselines identify few or no training-period recoverable target measurements, leaving retention undefined; BFHD yields stable retention across random seeds.Source: §D.3 · p. 14

D.4 Additional Results for Experiment 4: Ablation Results on CAS↔SNAP

On CAS↔SNAP, tied-weight MLP yields comparable coverage and stability, while removing output gating reduces stability despite similar coverage; other gate or feasibility variants degenerate. The study used de-identified datasets and conducted no new data collection or recruitment.

D.4 Additional Results for Experiment 4: Ablation Results on CAS↔SNAP

  • The ablation repeats the main-paper settings on CAS↔SNAP to check whether qualitative conclusions generalize to a second real-world pair.Source: §D.4 · p. 14
  • Replacing the invertible backbone with TWMLP yields comparable recoverable coverage and subset stability, whereas removing output gating reduces stability despite similar coverage.Source: §D.4 · p. 14, Table 9 · p. 15
  • An L0 gate penalty collapses to all-closed gating, while removing the hinge loss can produce all-open or unstable collapse, making subset stability uninformative.Source: §D.4 · pp. 14–15, Table 9 · p. 15

Ethical Statement

  • The study used de-identified public and access-controlled datasets and conducted no new data collection or human-subject recruitment.Source: Ethical Statement · p. 16

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