BioinstLab/bnet-ot-fusion

Sinkhorn-Based Optimal Transport Late Fusion for Breast Cancer Diagnosis

This is a cleaned reimplementation of the method in Asiedu Asare et al. (2026). The original notebooks, trained models, and intermediate outputs from the 2025 experiments were not retained, so results may not reproduce exactly.

Paper:

Asiedu Asare M, Acquah I, Appiah Yeboah B, Owusu E. Resilient Sinkhorn-Based Optimal Transport Late Fusion Framework for Breast Cancer Diagnosis. Cancer Informatics. 2026;25:1–15. doi:10.1177/11769351261420789

The framework combines two independently trained models, a histopathology image classifier (BreakHis) and a clinical risk-factor model (BCSC), at the level of their output probabilities. The fusion layer aligns the two predictions with entropy-regularized optimal transport and is designed to keep working when one modality is missing.

This repository implements the fusion layer and its evaluation as described in the paper. It does not include the two upstream models; it takes their predicted probabilities as input.

What is implemented

Paper	Code
Eq. 13: predictions as vectors in the probability simplex	otfusion.fusion.to_distribution
Eq. 14: modality mask m = [m_p, m_q]	otfusion.fusion.modality_mask (NaN = missing), or masks passed explicitly
Eq. 15: uniform substitution for a missing modality	otfusion.fusion.substitute_missing
Eq. 16: confidence-weighted fusion factor α	otfusion.fusion.dynamic_alpha
Eq. 17: cost matrix (divergence + clinical semantic penalty)	otfusion.fusion.cost_matrix, semantic_cost
Eq. 18: entropic OT, Sinkhorn-Knopp in the log domain	otfusion.sinkhorn.sinkhorn_log
Eq. 19: fused prediction from the row marginal of T*, outer-product fallback	otfusion.fusion.sinkhorn_fusion
Simulated modality dropout (Table 5)	otfusion.dropout.simulate_dropout
Calibrated fused output (Figs. 3–4)	otfusion.calibration (isotonic regression)
PR-AUC, recall, F1, Brier, 95% bootstrap CIs (1000 resamples), paired tests	otfusion.metrics
Decision curve analysis (Fig. 3)	otfusion.metrics.net_benefit, otfusion.plots.plot_decision_curve
Calibration curve, PR curve, average transport plan (Figs. 4–5)	otfusion.plots
Runtime per sample	recorded by otfusion.pipeline.run_evaluation

Default parameters

Defaults in FusionConfig are the values reported in the paper:

Parameter	Value	Meaning
fp_weight (w_p)	1.8	Semantic cost, entry (0, 1) of C_semantic
fn_weight (w_n)	1.2	Semantic cost, entry (1, 0) of C_semantic
alpha	0.1	Blend between divergence and semantic cost; "dynamic" uses Eq. 16
reg	0.15	Entropic regularization of the OT problem
max_iter	5000	Maximum Sinkhorn iterations
stop_thr	1e-9	Sinkhorn convergence threshold
eps	1e-8	Numerical stability constant in Eq. 16

Installation

git clone <this repository>
cd bnet-ot-fusion
pip install -e .            # or: pip install -r requirements.txt

Python 3.10 or later. Dependencies: NumPy, SciPy, scikit-learn, matplotlib.

Usage

As a library

import numpy as np
from otfusion import FusionConfig, sinkhorn_fusion

p_hist = np.array([0.92, 0.15, np.nan])   # histopathology P(malignant); NaN = missing
p_risk = np.array([0.40, 0.70, 0.65])     # clinical risk P(high risk)

result = sinkhorn_fusion(p_hist, p_risk, FusionConfig())
result.fused          # (N, 2) fused probability vectors
result.plans          # (N, 2, 2) transport plans
result.fallback       # samples where the outer-product fallback was used

Full evaluation

Save each model's predictions as .npy files (positive-class probabilities of shape (N,) or two-class vectors of shape (N, 2)), then:

python scripts/evaluate.py \
    --hist p_hist_test.npy --risk p_risk_test.npy --labels y_test.npy \
    --calib-hist p_hist_val.npy --calib-risk p_risk_val.npy --calib-labels y_val.npy \
    --out results/

This writes results.json (metrics with CIs for the fused model and baselines, paired comparisons, dropout results, runtime) and four figures to results/. Run python scripts/evaluate.py --help for all options.

Demo on synthetic data

python examples/synthetic_demo.py

Runs the whole pipeline on random synthetic predictions to show the inputs and outputs. The numbers it prints are unrelated to the paper.

Implementation notes

The paper's description leaves a few choices open. This implementation resolves them as follows:

• α (Eqs. 16–17). Eq. 16 defines a per-sample, confidence-weighted α, while the training section reports a fixed blending factor α = 0.1. The default is the fixed value; set alpha="dynamic" for Eq. 16.
• Regularization naming. The paper uses ε both for the entropic regularization in Eq. 18 and for a 1e-8 stability constant. Here they are separate: reg (0.15) for Eq. 18 and eps (1e-8) for Eq. 16.
• Sinkhorn solver. A batched log-domain Sinkhorn-Knopp solver is implemented directly in NumPy/SciPy. The fallback plan p ⊗ q is used when the final marginal violation exceeds fallback_tol (1e-6).
• Row marginal. Because Eq. 18 constrains T 1 = p̃, the row marginal read out in Eq. 19 equals the (mask-substituted) histopathology vector p̃ whenever Sinkhorn converges. This is covered by tests/test_fusion.py::test_eq19_row_marginal_equals_p_under_marginal_constraint.
• Calibration. The paper reports calibrated fused probabilities. Here an isotonic calibrator is fitted on a separate calibration split when provided, and otherwise cross-fitted (5 folds), so that no sample is calibrated with its own label.
• Dropout. By default each affected sample loses one modality chosen at random ("randomly omitting 1 input source"). Modes hist, risk and both are also available.
• Paired tests. paired_comparison scores both models on the same bootstrap resamples and reports the difference with a 95% CI, a bootstrap p-value, and a paired t-test on the replicates (as reported in the paper). The t-test p-value depends on the number of resamples, so the CI is the more interpretable summary.

Tests

pip install pytest
pytest

The tests check the Sinkhorn solution against a brute-force optimum, the marginal constraints, masking and uniform substitution, Eq. 16 limits, the cost matrix, the fallback, dropout masks, metrics against scikit-learn, decision-curve formulas, and an end-to-end pipeline run.

Data

The datasets are publicly available from their owners and are not redistributed here:

• BreakHis: http://www.inf.ufpr.br/vri/databases/BreaKHis_v1.tar.gz
• BCSC Risk Factors: https://www.bcsc-research.org/index.php/datasets/rf/risk-factor-dataset-download

Citation

@article{asieduasare2026sinkhorn,
  title   = {Resilient Sinkhorn-Based Optimal Transport Late Fusion Framework for Breast Cancer Diagnosis},
  author  = {Asiedu Asare, Michael and Acquah, Isaac and Appiah Yeboah, Benjamin and Owusu, Emmanuel},
  journal = {Cancer Informatics},
  volume  = {25},
  pages   = {1--15},
  year    = {2026},
  doi     = {10.1177/11769351261420789}
}

Contact

Michael Asiedu Asare, Biomedical Technologies Lab, Kwame Nkrumah University of Science and Technology. Corresponding author: Isaac Acquah (iacquah.coe@knust.edu.gh).