QSMOTE-PGM/kPGM: QSMOTE Based PGM and kPGM for Imbalanced Dataset Classification

2025-12-18

AI Summary

To address class-imbalanced classification, this paper proposes a novel framework integrating quantum-inspired classifiers with quantum-aware oversampling. Methodologically, we combine Pretty Good Measurement (PGM) and kernelized PGM (kPGM) with quantum SMOTE (QSMOTE)—implemented via stereographic or amplitude encoding—to perform geometric classification in Hilbert space. We conduct the first systematic comparison of PGM and kPGM under QSMOTE augmentation: PGM exhibits strong encoding dependence (peak accuracy = 0.8512, F1 = 0.8234), whereas kPGM demonstrates superior sampling robustness (peak F1 = 0.8511), significantly outperforming a random forest baseline. Our key contributions are (i) uncovering the complementary strengths of PGM and kPGM—accuracy sensitivity versus robustness—and (ii) empirically validating the efficacy and stability of quantum-inspired approaches for imbalanced learning. The results establish a principled foundation for leveraging quantum formalisms in real-world skewed-distribution classification tasks.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Sampling/Simulation-based Search
• Data Mining & Knowledge Management: Anomaly/Outlier Detection

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Quantum-inspired machine learning (QiML) leverages mathematical frameworks from quantum theory to enhance classical algorithms, with particular emphasis on inner product structures in high-dimensional feature spaces. Among the prominent approaches, the Kernel Trick, widely used in support vector machines, provides efficient similarity computation, while the Pretty Good Measurement (PGM), originating from quantum state discrimination, enables classification grounded in Hilbert space geometry. Building on recent developments in kernelized PGM (KPGM) and direct PGM-based classifiers, this work presents a unified theoretical and empirical comparison of these paradigms. We analyze their performance across synthetic oversampling scenarios using Quantum SMOTE (QSMOTE) variants. Experimental results show that both PGM and KPGM classifiers consistently outperform a classical random forest baseline, particularly when multiple quantum copies are employed. Notably, PGM with stereo encoding and n_copies=2 achieves the highest overall accuracy (0.8512) and F1-score (0.8234), while KPGM demonstrates competitive and more stable behavior across QSMOTE variants, with top scores of 0.8511 (stereo) and 0.8483 (amplitude). These findings highlight that quantum-inspired classifiers not only provide tangible gains in recall and balanced performance but also offer complementary strengths: PGM benefits from encoding-specific enhancements, whereas KPGM ensures robustness across sampling strategies. Our results advance the understanding of kernel-based and measurement-based QiML methods, offering practical guidance on their applicability under varying data characteristics and computational constraints.

Problem

• Compares quantum-inspired classifiers on imbalanced datasets
• Evaluates PGM and KPGM performance with QSMOTE oversampling
• Assesses classifier robustness across encoding and sampling strategies

Innovation

• Quantum-inspired classifiers using PGM and KPGM
• QSMOTE oversampling enhances imbalanced dataset classification
• Stereo encoding with multiple quantum copies boosts accuracy