Quantum-Inspired Stacked Concept Graph Model

• The paper introduces a novel framework that integrates quantum-inspired feature mapping and graph-based patient similarity to enhance diabetes risk prediction.
• It employs a hybrid architecture with autoencoder embeddings, k-NN concept graphs, and stacked ensemble learners, achieving high F1 (0.8933) and AUC (0.8699) scores.
• The model delivers scalable performance with efficient CPU inference (8.5 rows/second) and open-source reproducibility for clinical applications.

The Quantum-Inspired Stacked Integrated Concept Graph Model (QISICGM) is a machine learning framework that combines quantum-inspired representational techniques and stacked ensemble learning to improve predictive accuracy, efficiency, and interpretability in clinical risk modeling, specifically demonstrated for diabetes risk prediction. QISICGM integrates phase feature mapping, graph-based patient similarity, neighborhood sequence modeling, and multiple classical base learners in a unified pipeline, yielding performance metrics that surpass traditional approaches. The design draws from both quantum information theory and concepts from graph-based learning to achieve superior separability and robustness while emphasizing interpretability and open-source reproducibility (II, 12 Sep 2025).

1. Model Architecture

QISICGM comprises a two-stage process:

A. Quantum-Inspired Feature Processing

• Raw tabular data (augmented PIMA Indians Diabetes dataset) undergoes imputation, feature engineering, and normalization.
• Each scalar feature $x_i$ is transformed into a two-dimensional phase feature via:

$$\varphi(x_i) = \begin{bmatrix} \cos(\alpha x_i) \ \sin(\alpha x_i) \end{bmatrix}$$

where $\alpha$ is a scaling parameter learned during training. This operation is reminiscent of amplitude embedding in quantum machine learning models and expands the feature space.

B. Self-Improving Concept Graph & Stacked Ensemble

• Autoencoder-based patient embeddings are computed and used to build a k-nearest neighbors (k-NN) concept graph, clustering similar patients and enabling neighborhood aggregation.
• Neighborhood sequence modeling captures interactions among patient embeddings by applying either transformer blocks with multi-head attention or convolutional neural networks (CNNs).
• Base learners include Random Forests (RF), Extra Trees (ET), transformer modules, CNNs, and Feed-Forward Neural Networks (FFNN).
• Each base model's predictions are calibrated using isotonic regression, and a logistic regression meta-learner combines meta-features (probabilities, logits, vote statistics) for final prediction.
• The full pipeline is implemented with 5-fold cross-validation, with out-of-fold (OOF) and test evaluations.

Architecture flow can be summarized as:

Data → Imputation & Feature Engineering │ Phase Feature Map: ϕ(xᵢ) │ Embeddings (Autoencoder) → k-NN Concept Graph │ Neighborhood Sequence Modeling (Transformer/CNN) │ Base Learners (RF, ET, Transformer, CNN-Seq, FFNN) │ Meta-Learner (Logistic Regression) → Final Prediction

2. Quantum-Inspired Components

A. Phase Feature Mapping

• The $[\cos(\alpha x_i), \sin(\alpha x_i)]$ mapping encodes scalar data into a higher-dimensional "phase space."
• This mapping is analogous to how classical features are lifted into amplitude or phase domains in quantum machine learning, enhancing the model's ability to distinguish complex, nonlinear relationships.

B. Neighborhood Sequence Modeling

• After constructing a k-NN graph over patient embeddings, sequences of neighboring patients are extracted.
• Transformers use multi-head attention ($$\text{Attention}(Q, K, V) = \text{softmax}(QK^\top/\sqrt{d_k}) V$$) to jointly process neighbor sequences, simulating quantum entanglement among concept nodes.
• CNNs can alternatively be used to process local interaction patterns within neighbor sequences.

C. Self-Improving Graph Construction

• The concept graph is refined iteratively to minimize

$L = -\sum [y \log(\hat{y}) + (1-y)\log(1-\hat{y})]$

analogous to energy minimization in quantum annealing, converging to low-energy (optimal similarity) states.

3. Performance Metrics

QISICGM evaluated on the augmented PIMA Diabetes dataset (2,768 samples, including 2,000 synthetic cases for class balance) achieves:

• Out-of-Fold (OOF) F1 score: 0.8933
• AUC: 0.8699

For comparison:

Model	OOF F1	AUC
QISICGM	0.8933	0.8699
Random Forest	~0.821	~0.803
Other Ensembles	lower	lower

Low variance across five folds is demonstrated. Detailed performance tables in the paper show per-fold accuracy and calibration scores (Brier score = 0.12), with probability distributions well-calibrated for reliable clinical decision support.

4. Computational Efficiency and Scalability

• QISICGM achieves 8.5 rows/second inference on CPU, indicating suitability for hospital and clinical environments lacking GPU acceleration.
• Efficiency stems from vectorized phase mapping and optimized implementation in NumPy and PyTorch.
• The modular architecture (separating quantum-inspired preprocessing from ensemble predictions) ensures scalability as model complexity or dataset size increase.

5. Theoretical Underpinnings

• Quantum Information Theory: The feature mapping leverages the encoding strategies used in quantum circuits, facilitating nonlinear transformation of classical input into a richer space.
• Graph Theory & Quantum Annealing: The concept graph is constructed and refined with techniques similar to quantum annealing, improving clustering and neighborhood modeling among patients.
• Stacked Generalization: Robust generalization is achieved by integrating diverse model types (i.e., tree-based, sequential, and feed-forward learners), which is theoretically justified by the principles of stacked ensemble learning.

6. Code Availability and Reproducibility

• The QISICGM implementation (v1.0.0) is open-source and available at https://github.com/keninayoung/QISICGM.
• Full documentation and pipeline are provided (main entry: qisicgm_stacked.py), including preprocessing, cross-validation, calibration, and model retraining scripts.
• Open release ensures reproducibility and facilitates further clinical and research adaptation.

7. Visualizations and Interpretability

• Calibration diagrams and probability histograms indicate reliable, well-calibrated output probabilities.
• Concept graph visualizations for each cross-validation fold reveal distinct clusters for diabetic and non-diabetic patients, confirming effective patient similarity modeling.
• Empirical results and performance tables further reinforce model interpretability and diagnostic trust.

Conclusion

QISICGM exemplifies the integration of quantum-inspired feature mapping with graph-based neighborhood sequence modeling and stacked ensemble prediction to deliver high accuracy, robust calibration, and computational efficiency for diabetes risk prediction. The model's open-source implementation, modular design, and interpretability features position it as a promising benchmark for trustworthy AI in clinical triage and predictive modeling. The combination of phase-lifted features and concept graph aggregation leverages quantum analogies to surpass traditional risk prediction models while remaining scalable and transparent for clinical deployment.