Quantum-Inspired Optimization Process for Data Imputation

TL;DR

The paper tackles missing data in critical domains by introducing a quantum-inspired imputation framework that fuses classical PCA with quantum rotations to reconstruct missing values while preserving statistical diversity. It enforces bounds within $[\mu_j-2\sigma_j,\mu_j+2\sigma_j]$ and uses gradient-free optimizers (Differential Evolution, COBYLA, Simulated Annealing) to fine-tune rotation angles, yielding more realistic distributions than classical imputations. Evaluations on the UCI Diabetes dataset show substantial improvements in distributional fidelity and variability, as evidenced by KS tests around $0.18$–$0.22$ and sizable Wasserstein-distance changes for several features, with notable impact on features like Glucose, Insulin, and SkinThickness. The approach offers a scalable, data-integrity-preserving path for imputation in healthcare and AI pipelines, with clear potential for future quantum hardware to further accelerate optimization and exploration of imputations.

Abstract

Data imputation is a critical step in data pre-processing, particularly for datasets with missing or unreliable values. This study introduces a novel quantum-inspired imputation framework evaluated on the UCI Diabetes dataset, which contains biologically implausible missing values across several clinical features. The method integrates Principal Component Analysis (PCA) with quantum-assisted rotations, optimized through gradient-free classical optimizers -COBYLA, Simulated Annealing, and Differential Evolution to reconstruct missing values while preserving statistical fidelity. Reconstructed values are constrained within +/-2 standard deviations of original feature distributions, avoiding unrealistic clustering around central tendencies. This approach achieves a substantial and statistically significant improvement, including an average reduction of over 85% in Wasserstein distance and Kolmogorov-Smirnov test p-values between 0.18 and 0.22, compared to p-values > 0.99 in classical methods such as Mean, KNN, and MICE. The method also eliminates zero-value artifacts and enhances the realism and variability of imputed data. By combining quantum-inspired transformations with a scalable classical framework, this methodology provides a robust solution for imputation tasks in domains such as healthcare and AI pipelines, where data quality and integrity are crucial.

Figures (13)

• Figure 1: Schematic diagram of the overall process of Imputation.
• Figure 2: Missing vs Nonmissing values recordwise
• Figure 3: Featurewise Missing values
• Figure 4: KDE of Glucose: Original vs. Rotated Datasets.
• Figure 5: KDE of BloodPressure: Original vs. Rotated Datasets