pith. sign in

arxiv: 2512.16960 · v2 · pith:222VDYXGnew · submitted 2025-12-18 · 💻 cs.LG · quant-ph

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

Bikash K. Behera , Giuseppe Sergioli , Roberto Giuntini This is my paper

Pith reviewed 2026-05-16 21:54 UTC · model grok-4.3

classification 💻 cs.LG quant-ph
keywords quantum-inspired machine learningimbalanced datasetsQSMOTEpretty good measurementoversamplingclassificationcustomer churnminority class
0
0 comments X

The pith

Quantum-inspired oversampling paired with pretty good measurement classifiers raises recall on imbalanced churn data over random forest.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that three QSMOTE variants built on quantum-inspired similarity measures, when combined with PGM and kernelized PGM classifiers, produce higher recall and balanced F1 scores than a classical random forest baseline on the Telco Customer Churn dataset. Stereo encoding with two quantum copies in the PGM configuration reaches the strongest recorded result. The authors show that performance rises steadily as the number of copies increases, particularly for the minority class. A reader would care because many practical classification tasks, such as churn or fraud detection, suffer when rare positive cases are under-represented in training.

Core claim

The authors establish that QSMOTE-enhanced PGM and KPGM classifiers outperform the classical Random Forest baseline on the Telco Customer Churn dataset, with PGM under stereo encoding and two copies attaining the highest accuracy of 0.8512 and F1-score of 0.8234, while KPGM provides stable results across encodings, and performance improves with more quantum copies.

What carries the argument

QSMOTE variants using KNN-based, Fidelity-based, and Margin-based quantum-inspired similarity measures, integrated with PGM and kernelized PGM under amplitude and stereo encodings.

If this is right

  • Increasing the number of quantum copies systematically raises classification performance, especially for minority-class detection.
  • PGM with stereo encoding delivers the highest accuracy and F1 among the tested configurations.
  • KPGM exhibits more stable accuracy across the three QSMOTE variants than PGM does.
  • The combination of quantum-inspired oversampling and measurement-based classification improves results on imbalanced learning tasks.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The observed gains might extend to other imbalanced problems such as medical diagnosis or fraud detection if the same encoding and copy-count patterns hold.
  • KPGM's greater stability across variants could make it the default choice when data distributions vary between training and deployment.
  • Controlled experiments that vary only the imbalance ratio while holding feature distributions fixed would isolate whether the quantum similarity measures or the encoding choice drives most of the improvement.

Load-bearing premise

The quantum-inspired similarity measures in the three QSMOTE variants genuinely improve minority-class representation in a way that generalizes beyond the specific encodings and dataset tested.

What would settle it

Repeating the full experimental protocol on a second imbalanced dataset such as credit-card fraud detection and finding no consistent lift in recall or balanced F1 over random forest would falsify the central claim.

Figures

Figures reproduced from arXiv: 2512.16960 by Bikash K. Behera, Giuseppe Sergioli, Roberto Giuntini.

Figure 1
Figure 1. Figure 1: Schematic illustration of the three proposed QSMOTE variants. (a) KNN-based QSMOTE interpolates between a sample and its [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: RF baseline performance across QSMOTE variants. [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: F1 (mean ± std) by QSMOTE variant for PGM with amplitude encoding. (a) PGM (Stereo), n copies = 1 (b) PGM (Stereo), n copies = 2 [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: F1 (mean ± std) by QSMOTE variant for PGM with stereo encoding [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Effect of n copies on PGM performance across QSMOTE variants. (a) KPGM (Amplitude), n copies = 1 (b) KPGM (Amplitude), n copies = 2 [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: F1 (mean ± std) by QSMOTE variant for KPGM with amplitude encoding. (a) KPGM (Stereo), n copies = 1 (b) KPGM (Stereo), n copies = 2 [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: F1 (mean ± std) by QSMOTE variant for KPGM with stereo encoding [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Effect of n copies on KPGM performance across QSMOTE variants. (a) PGM (Amplitude), n copies = 1 (b) PGM (Amplitude), n copies = 2 (c) PGM (Stereo), n copies = 1 (d) PGM (Stereo), n copies = 2 [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Precision-Recall tradeoffs for PGM under amplitude and stereo encodings with [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Precision-Recall tradeoffs for KPGM under amplitude and stereo encodings with [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
read the original abstract

Quantum-inspired machine learning (QiML) employs mathematical principles from quantum theory, such as Hilbert-space representations and quantum state discrimination, to enhance classical learning algorithms. In this work, we investigate the integration of Quantum Synthetic Minority Oversampling Technique (QSMOTE) variants with two quantum-inspired classifiers: the Pretty Good Measurement (PGM) classifier and the kernelized Pretty Good Measurement (KPGM) classifier. We propose and analyze three QSMOTE variants, namely KNN-based, Fidelity-based, and Margin-based QSMOTE, designed to improve minority-class representation in imbalanced datasets through quantum-inspired similarity and sampling mechanisms. A unified theoretical and empirical comparison of PGM and KPGM is presented under amplitude and stereo encoding strategies with multiple quantum copies. Experimental evaluations on the Telco Customer Churn dataset demonstrate that the proposed quantum-inspired approaches consistently outperform a classical Random Forest baseline, particularly in terms of recall and balanced F1-score. Among all configurations, PGM with stereo encoding and n_{copies}=2 achieves the best performance with an accuracy of 0.8512 and an F1-score of 0.8234, while KPGM exhibits competitive and more stable behavior across different QSMOTE variants, reaching accuracies of 0.8511 under stereo encoding and 0.8483 under amplitude encoding. The results further show that increasing the number of quantum copies systematically improves classification performance, especially for minority-class detection. This work highlights the effectiveness of combining quantum-inspired oversampling and classification strategies for imbalanced learning, while providing practical insights into the complementary strengths of measurement-based and kernel-based quantum-inspired machine learning frameworks.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes three QSMOTE variants (KNN-based, Fidelity-based, Margin-based) that incorporate quantum-inspired similarity measures for oversampling minority classes, then integrates them with Pretty Good Measurement (PGM) and kernelized PGM (KPGM) classifiers under amplitude and stereo encodings with multiple quantum copies. On the Telco Customer Churn dataset the authors report that these quantum-inspired pipelines consistently outperform an untuned classical Random Forest baseline, with the strongest result being PGM + stereo encoding + n_copies=2 (accuracy 0.8512, F1 0.8234); KPGM is described as more stable across variants, and performance is said to improve with additional copies.

Significance. If the reported gains prove robust under proper controls, the work would supply a concrete demonstration that quantum-inspired similarity and measurement primitives can improve minority-class handling in imbalanced classification. The unified treatment of PGM versus KPGM across encodings offers a useful comparative framework, and the explicit dependence on n_copies provides a tunable, interpretable axis. However, the current single-dataset, single-baseline evaluation limits the strength of any broader claim about the value of the quantum-inspired components.

major comments (3)
  1. [Experimental Evaluations] Experimental Evaluations section: performance figures (e.g., accuracy 0.8512, F1 0.8234) are given as single point estimates with no error bars, standard deviations across random seeds, or statistical significance tests, rendering the claim of “consistent outperformance” unverifiable from the supplied information.
  2. [Experimental Evaluations] Experimental Evaluations section: the only baseline is an untuned Random Forest; no head-to-head results appear for classical SMOTE, ADASYN, or Borderline-SMOTE under identical data splits and classifier, so it is impossible to isolate whether observed gains arise from the quantum-inspired similarity measures or from oversampling volume alone.
  3. [Abstract and §4] Abstract and §4: the evaluation is confined to a single public dataset (Telco Customer Churn); without results on additional imbalanced benchmarks the generalization of the QSMOTE similarity mechanisms remains an open question.
minor comments (2)
  1. [Throughout] Notation for the number of copies is written inconsistently as n_copies and n_{copies}; adopt a single LaTeX form throughout.
  2. [Abstract] The abstract states that KPGM reaches 0.8511 under stereo encoding; the corresponding table or figure row should be explicitly referenced so readers can locate the exact configuration.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major point below and have revised the manuscript to strengthen the experimental section.

read point-by-point responses

  1. Referee: [Experimental Evaluations] Experimental Evaluations section: performance figures (e.g., accuracy 0.8512, F1 0.8234) are given as single point estimates with no error bars, standard deviations across random seeds, or statistical significance tests, rendering the claim of “consistent outperformance” unverifiable from the supplied information.

    Authors: We agree that single-point estimates limit verifiability. In the revised manuscript we rerun all experiments across 10 random seeds, report means with standard deviations, and include paired t-tests against the baseline to support the outperformance claims. revision: yes

  2. Referee: [Experimental Evaluations] Experimental Evaluations section: the only baseline is an untuned Random Forest; no head-to-head results appear for classical SMOTE, ADASYN, or Borderline-SMOTE under identical data splits and classifier, so it is impossible to isolate whether observed gains arise from the quantum-inspired similarity measures or from oversampling volume alone.

    Authors: The referee correctly notes the need for stronger baselines. We have added head-to-head comparisons with classical SMOTE, ADASYN, and Borderline-SMOTE using identical splits and the Random Forest classifier. These results demonstrate that the quantum-inspired QSMOTE variants yield further gains beyond standard oversampling. revision: yes

  3. Referee: [Abstract and §4] Abstract and §4: the evaluation is confined to a single public dataset (Telco Customer Churn); without results on additional imbalanced benchmarks the generalization of the QSMOTE similarity mechanisms remains an open question.

    Authors: We acknowledge the single-dataset limitation. The revised manuscript now includes results on the Credit Card Fraud Detection dataset. The performance advantages of QSMOTE-PGM and QSMOTE-KPGM remain consistent, supporting broader applicability of the quantum-inspired similarity measures. revision: yes

Circularity Check

0 steps flagged

No significant circularity; empirical results stand on external baseline comparison

full rationale

The manuscript proposes three QSMOTE variants (KNN-, Fidelity-, and Margin-based) and integrates them with PGM and KPGM classifiers under amplitude and stereo encodings. It then reports direct experimental outcomes on the named public Telco Customer Churn dataset, comparing against an untuned classical Random Forest baseline. No mathematical derivation chain, parameter-fitting step, or uniqueness theorem is invoked that reduces any reported performance figure to a fitted input or self-citation by construction. The central claims rest on observable accuracy, recall, and F1 values obtained from the external dataset and classifier, rendering the work self-contained.

Axiom & Free-Parameter Ledger

1 free parameters · 0 axioms · 0 invented entities

Based solely on the abstract, the central claims rest on standard quantum-inspired concepts (Hilbert-space representations, fidelity, state discrimination) treated as background; no new free parameters beyond the tunable number of copies, no invented entities, and no ad-hoc axioms are explicitly introduced.

free parameters (1)
  • n_copies
    Number of quantum state copies is varied experimentally and reported to improve performance, with best results at 2.

pith-pipeline@v0.9.0 · 5613 in / 1453 out tokens · 54801 ms · 2026-05-16T21:54:20.445814+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

19 extracted references · 19 canonical work pages · 1 internal anchor

  1. [1]

    An introduction to quantum machine learning,

    M. Schuld, I. Sinayskiy, and F. Petruccione, “An introduction to quantum machine learning,”Contemporary Physics, vol. 56, no. 2, pp. 172–185, 2015. [Online]. Available: https://doi.org/10.1080/00107514. 2014.964942

    work page doi:10.1080/00107514 2015

  2. [2]

    Quantum machine learning,

    J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. Lloyd, “Quantum machine learning,”Nature, vol. 549, no. 7671, pp. 195–202, 2017

    work page 2017

  3. [3]

    Pretty good measurement,

    P. Hausladen and W. K. Wootters, “Pretty good measurement,”Journal of Modern Optics, vol. 41, no. 12, pp. 2385–2390, 1994

    work page 1994

  4. [4]

    A new quantum approach to binary classification,

    G. Sergioli, R. Giuntini, and H. Freytes, “A new quantum approach to binary classification,”PLOS ONE, vol. 14, no. 3, p. e0213100, 2019

    work page 2019

  5. [5]

    Quantum-inspired algorithm for direct multi-class classification,

    R. Giuntini, F. Holik, D. K. Park, H. Freytes, C. Blank, and G. Sergioli, “Quantum-inspired algorithm for direct multi-class classification,” Applied Soft Computing, vol. 134, p. 109956, Feb. 2023. [Online]. Available: https://doi.org/10.1016/j.asoc.2022.109956

    work page doi:10.1016/j.asoc.2022.109956 2023

  6. [6]

    Multi-class classification based on quantum state discrimination,

    R. Giuntini, A. C. G. Arango, H. Freytes, F. H. Holik, and G. Sergioli, “Multi-class classification based on quantum state discrimination,” Fuzzy Sets and Systems, vol. 467, p. 108509, 2023. [Online]. Available: https://doi.org/10.1016/j.fss.2023.03.012

    work page doi:10.1016/j.fss.2023.03.012 2023

  7. [8]

    Quantum classification

    [Online]. Available: https://arxiv.org/abs/0809.0444

    work page internal anchor Pith review Pith/arXiv arXiv

  8. [9]

    A quantum-inspired version of the nearest mean classifier,

    G. Sergioli, E. Santucci, L. Didaci, J. A. Miszczak, and R. Giuntini, “A quantum-inspired version of the nearest mean classifier,”Soft Computing, vol. 22, no. 3, pp. 691–705, 2018. [Online]. Available: https://doi.org/10.1007/s00500-016-2478-2

    work page doi:10.1007/s00500-016-2478-2 2018

  9. [10]

    A new quantum approach to binary classification,

    G. Sergioli, R. Giuntini, and H. Freytes, “A new quantum approach to binary classification,”PLOS ONE, vol. 14, no. 5, p. e0216224,

    work page

  10. [11]

    Available: https://journals.plos.org/plosone/article?id= 10.1371/journal.pone.0216224

    [Online]. Available: https://journals.plos.org/plosone/article?id= 10.1371/journal.pone.0216224

    work page doi:10.1371/journal.pone.0216224

  11. [12]

    Quantum detection and estimation theory,

    C. W. Helstrom, “Quantum detection and estimation theory,”Journal of Statistical Physics, vol. 1, no. 2, pp. 231–252, 1969. [Online]. Available: https://doi.org/10.1007/BF01007479

    work page doi:10.1007/bf01007479 1969

  12. [13]

    Designing optimal quantum detectors via semidefinite programming,

    Y . C. Eldar, A. Megretski, and G. C. Verghese, “Designing optimal quantum detectors via semidefinite programming,”IEEE Transactions on Information Theory, vol. 49, no. 4, pp. 1007–1012, April 2003. [Online]. Available: https://ieeexplore.ieee.org/document/1193807

    work page arXiv 2003

  13. [14]

    Quantum- inspired classification based on quantum state discrimination,

    E. Z. Cruzeiro, C. D. Mol, S. Massar, and S. Pironio, “Quantum- inspired classification based on quantum state discrimination,”Quantum Machine Intelligence, vol. 6, no. 79, 2024. [Online]. Available: https://doi.org/10.1007/s42484-024-00216-6

    work page doi:10.1007/s42484-024-00216-6 2024

  14. [15]

    IEEE Trans

    H. He and E. A. Garcia, “Learning from imbalanced data,”IEEE Transactions on Knowledge and Data Engineering, vol. 21, no. 9, pp. 1263–1284, 2009. [Online]. Available: https://doi.org/10.1109/TKDE. 2008.239

    work page doi:10.1109/tkde 2009

  15. [16]

    The class imbalance problem: A systematic study,

    N. Japkowicz and S. Stephen, “The class imbalance problem: A systematic study,”Intelligent Data Analysis, vol. 6, no. 5, pp. 429–449,

    work page

  16. [17]

    Intelligent Data Analysis6(5), 429–449 (2002) https://doi.org/10.3233/IDA-2002-6504

    [Online]. Available: https://doi.org/10.3233/IDA-2002-6504

    work page doi:10.3233/ida-2002-6504 2002

  17. [18]

    SMOTE: synthetic minority over-sampling technique,

    N. V . Chawla, K. W. Bowyer, L. O. Hall, and W. P. Kegelmeyer, “Smote: Synthetic minority over-sampling technique,”Journal of Artificial Intelligence Research, vol. 16, pp. 321–357, 2002. [Online]. Available: https://doi.org/10.1613/jair.953

    work page doi:10.1613/jair.953 2002

  18. [19]

    A quantum ap- proach to synthetic minority oversampling technique (smote),

    N. Mohanty, B. K. Behera, C. Ferrie, and P. Dash, “A quantum ap- proach to synthetic minority oversampling technique (smote),”Quantum Machine Intelligence, vol. 7, no. 1, p. 38, 2025

    work page 2025

  19. [20]

    Telco customer churn dataset,

    Blastchar, “Telco customer churn dataset,” https://www.kaggle.com/ datasets/blastchar/telco-customer-churn, 2017, accessed: July 2025

    work page 2017