Close to Reality: Interpretable and Feasible Data Augmentation for Imbalanced Learning

Matheus Camilo da Silva; Gabriel Gustavo Costanzo; Andrea de Lorenzo; Sylvio Barbon Junior

cs.LGMar 14, 2026

Close to Reality: Interpretable and Feasible Data Augmentation for Imbalanced Learning

Authors: Matheus Camilo da Silva, Gabriel Gustavo Costanzo, Andrea de Lorenzo, Sylvio Barbon Junior

Organizations: Department of Mathematics, Computer Science and Geosciences, University of Trieste, Piazzale Europa, 1, 34127 Trieste TS, Italy.

Abstract

Many machine learning classification tasks involve imbalanced datasets, which are often subject to over-sampling techniques aimed at improving model performance. However, these techniques are prone to generating unrealistic or infeasible samples. Furthermore, they often function as black boxes, lacking interpretability in their procedures. This opacity makes it difficult to track their effectiveness and provide necessary adjustments, and they may ultimately fail to yield significant performance improvements. To bridge this gap, we introduce the Decision Predicate Graphs for Data Augmentation (DPG-da), a framework that extracts interpretable decision predicates from trained models to capture domain rules and enforce them during sample generation. This design ensures that over-sampled data remain diverse, constraint-satisfying, and interpretable. In experiments on synthetic and real-world benchmark datasets, DPG-da consistently improves classification performance over traditional over-sampling methods, while guaranteeing logical validity and offering clear, interpretable explanations of the over-sampled data.

Figures & tables

Panel of Figure 1 — Figure 1: DPG structure showing predicates as nodes and class leaves.

Figure 2: Workflow of the proposed DPG-da. Constraints extracted from DPGs guide the optimization for valid and diverse synthetic samples.

Feature	$\boldsymbol{\Delta^{0\rightarrow 1}}$	$\boldsymbol{\Delta^{1\rightarrow 2}}$	$\boldsymbol{\Delta^{2\rightarrow 3}}$
$x_{1}$ (Age)	$+2$	$+3$	$+2$
$x_{2}$ (Income)	$+2$	$+3$	$+5$
$x_{3}$ (Credit Score)	$-10$	$-5$	$-15\ (\times)$
$x_{4}$ (Number of Children)	$0$	$+1$	$0$

Table 1: Feature-wise changes (

\Delta x_{i}

) between successive generations of the GA in the DPG-da augmentation process. A violation of constraint

C_{3}

occurs in generation 3 (signed by

\times

Figure 3: Heatmap of normalized constraint violation rates per over-sampling method and dataset. Violation rate is computed as the number of violations divided by the number of synthesized samples, averaged across repeated runs.

Figure 4: Mean classification performance across augmentation methods and sampling percentages. Red background areas indicate methods that violated constraints (DE, SMOTE-LVQ, SMOTE-POLYNOM, and SMOTE-SVM). The dashed line indicates the average performance of the classifiers on the original datasets without augmentation.

Figure 5: Critical difference diagram for F1-score performance. Methods not connected by a bar differ significantly (Nemenyi test,

\alpha=0.05

, CD = 1.167).

Figure 6: Log scaled Time performance of the augmentation methods.

Figure 7: Heatmap of the evolutive process in the Wisconsin dataset. Showcasing the change ( $\Delta$ ) in feature values between generations in the GA.

Figure 8: Interpretable feature changes during the genetic algorithm evolution. The top row shows Pima (left) and Ecoli (right), while the bottom row shows Wisconsin. Each horizontal bar represents the absolute difference of a feature from the first to the last generation. The white numbers inside the bars indicate the magnitude of the change, the black numbers outside the bars indicate the number of generations with non-zero change, and the text to the right shows the query-to-augmented transformation for each feature.

Appendix figures & tables16 assets

Supplementary material from the paper’s appendix.

Appendix

Method	Description
ROS	Random over-sampling; simple, replicates existing minority instances.
SMOTE	Interpolation-based over-sampling [ Chawla et al., 2002 ] ; improves class balance.
SMOTE-ENN	SMOTE followed by Edited Nearest Neighbors [ Batista et al., 2004 ] ; reduces noise.
SMOTE-SVM	Focuses augmentation near decision boundaries [ Bunkhumpornpat et al., 2009 ] .
MSMOTE	Targets difficult minority regions for improved discrimination [ Hu et al., 2009 ] .
SMOTE-POLYNOM	Captures non-linear feature relationships [ Gazzah and Essoukri Ben Amara, 2008 ] .

Appendix

Table 2: Summary of over-sampling methods compared in this study. Methods range from classical interpolation-based techniques to recent generative approaches.

Figure 9: Top-performing ablation weight configurations for the optimization function, ranked by macro F1-score. Each configuration is denoted by its

(w1,w2,w3)

tuple corresponding to distance, sparsity, and constraints factors. The results indicate which combinations yield the highest predictive performance across all datasets.

Name	Ratio	#Samples	#Features
Healthcare	3:1	1,000	4
Finance	1:1	1,000	4
Quality Control	2:1	1,000	4
Fraud Detection	3:1	1,000	4
Energy	1:1	1,000	3
Education	1:1	1,000	3

Appendix

Table 3: Overview of datasets curated for the benchmark of violations

Name	Ratio	#Samples	#Features
ecoli	8.6:1	336	7
optical digits	9.1:1	5,620	64
satimage	9.3:1	6,435	36
pen digits	9.4:1	10,992	16
abalone	9.7:1	4,177	8
sick euthyroid	9.8:1	3,162	25

Appendix

Table 4: Summary of the UCI imbalanced benchmarking datasets used in the experiments on Classifier performance. Ratio refers to the imbalance level.

Dataset	Class	Feature Ranges / Constraints
Education	negative	Attendance: [50.68, 99.96]; Grades: [52.51, 99.56]; StudyHours: [0.47, 19.72]
	positive	Attendance: [50.68, 99.96]; Grades: [52.51, 99.56]; StudyHours: [0.47, 19.72]
Energy	negative	Usage: [0.52, 2.47]; Baseline: [103.32, 495.35]; Voltage: [190.39, 249.85]
	positive	Usage: [0.52, 2.44]; Baseline: [103.32, 498.23]; Voltage: [191.02, 249.85]
Finance	negative	CreditScore: [308.5, 845.0]; Income: [21340.5, 149246.5]; NumChildren: [0.5, 4.5]
	positive	CreditScore: [309.0, 845.0]; Income: [21755.5, 149246.5]; NumChildren: [0.5, 4.5]

Appendix

Table 5: Model-derived constraints extracted by DPG-da for the violation set of datasets.

Figure 10: Pairwise scatter plots of SMOTE-LVQ augmented samples from the Wisconsin dataset. Blue circles indicate valid samples within feature constraints, red crosses indicate samples violating at least one feature range. Green rectangles show the valid region for each feature pair.

Figure 11: Heatmap of feature-wise changes ( $\Delta$ ) during the GA on the Ecoli dataset. Early generations explore a broad range of features, with substantial variation across most attributes. As evolution proceeds, the process converges, reflecting stabilization of the candidate samples within the feasible region.

Figure 12: Heatmap of feature-wise changes ( $\Delta$ ) during the GA on the Pima dataset. Unlike Ecoli, the augmentation converges rapidly by modifying exclusively the glucose feature. This highlights a highly localized and interpretable transformation path, where minority samples are generated through a single, domain-relevant attribute shift.

Method	MD $\pm$ MAD	MR
DPG-da	0.757 $\pm$ 0.109	2.531
TVAE	0.719 $\pm$ 0.144	3.704
ROS	0.728 $\pm$ 0.131	3.975
SMOTE	0.708 $\pm$ 0.130	4.506
CTGAN	0.722 $\pm$ 0.135	5.272
COPULA-GAN	0.691 $\pm$ 0.158	5.025

Appendix

Table 6: Detailed statistical results (MD, MAD, MR) complementing the CD diagram in Figure 5

Figure 13: Baseline versus DPG-da macro F1-score comparison across datasets. Each point corresponds to one dataset, and the diagonal indicates equal performance.

Dataset	Baseline F1	DPG-da F1
car_eval_34	0.893	0.862
letter_img	0.940	0.908
mammography	0.790	0.554
pen_digits	0.951	0.923
protein_homo	0.897	0.850
sick_euthyroid	0.829	0.760

Appendix

Table 7: Datasets for which the baseline (0% augmentation) achieves higher average F1-score than DPG-da.

Figure 14: Distribution of precision (left) and recall (right) scores across augmentation methods and levels, averaged over datasets and classifiers. Red-shaded areas indicate methods that produced constraint violations. Both panels share a common y-axis labeled “Score” to facilitate comparison between metrics.

Dataset	DE	SMOTE-ENN	MSMOTE	SMOTE-LVQ	COPULA-GAN	CTGAN	SMOTE-POLYNOM	SMOTE	ROS	TVAE	SMOTE-SVM	DPG-da
abalone	0.600	0.602	0.614	0.584	0.588	0.599	0.601	0.594	0.593	0.598	0.608	0.566
abalone_19	0.487	0.505	0.535	0.492	0.497	0.525	0.511	0.474	0.509	0.505	0.536	0.627
arrhythmia	0.639	0.659	0.590	0.617	0.629	0.672	0.651	0.716	0.617	0.654	0.663	0.860
car_eval_34	0.821	0.829	0.823	0.866	0.874	0.889	0.872	0.870	0.881	0.921	0.882	0.862
car_eval_4	0.853	0.866	0.897	0.885	0.902	0.900	0.895	0.917	0.896	0.934	0.907	0.903
coil_2000	0.523	0.522	0.530	0.529	0.520	0.521	0.530	0.537	0.533	0.526	0.534	0.619

Appendix

Table 8: F1-Score by dataset and over-sampling method, averaged over augmentation levels. The highest performance per dataset is in bold.

Dataset	0%				15%			30%			50%
	RF	DT	LR	kNN	DT	LR	kNN	DT	LR	kNN	DT	LR	kNN
abalone	0.615	0.588	0.483	0.560	0.614	0.476	0.603	0.598	0.476	0.612	0.621	0.476	0.624
abalone_19	0.497	0.510	0.498	0.498	0.634	0.564	0.748	0.640	0.505	0.642	0.648	0.502	0.757
arrhythmia	0.573	0.793	0.620	0.485	0.859	0.881	0.798	0.834	0.881	0.801	0.859	0.892	0.934
car_eval_34	0.810	0.957	0.956	0.765	0.915	0.952	0.685	0.923	0.960	0.668	0.923	0.948	0.787
car_eval_4	0.827	0.988	0.922	0.503	0.974	0.895	0.828	1.000	0.895	0.818	0.974	0.922	0.818

Appendix

Table 9: DPG-da Macro F1-score for each dataset, classifiers, and augmentation percentage. Each row corresponds to one dataset, and columns are grouped by augmentation percentage (0%, 15%, 30%, 50%).

Figure 15: Spearman correlation between dataset characteristics ( Number of Features , Number of Instances , and Imbalance Ratio ) and two aspects: left the F1-score performance of the augmentation methods and right their runtime .

Dataset	RF (0%)	DE	SMOTE-ENN	MSMOTE	SMOTE-LVQ	COPULA-GAN	CTGAN	SMOTE-POLYNOM	SMOTE	ROS	TVAE	SMOTE-SVM	DPG-da
abalone	0.615	0.600	0.602	0.614	0.584	0.588	0.599	0.601	0.594	0.593	0.598	0.608	0.566
abalone_19	0.497	0.487	0.505	0.535	0.492	0.497	0.525	0.511	0.474	0.509	0.505	0.536	0.627
arrhythmia	0.573	0.639	0.659	0.590	0.617	0.629	0.672	0.651	0.716	0.617	0.654	0.663	0.860
car_eval_34	0.810	0.821	0.829	0.823	0.866	0.874	0.889	0.872	0.870	0.881	0.921	0.882	0.862
car_eval_4	0.827	0.853	0.866	0.897	0.885	0.902	0.900	0.895	0.917	0.896	0.934	0.907	0.903
coil_2000	0.537	0.523	0.522	0.530	0.529	0.520	0.521	0.530	0.537	0.533	0.526	0.534	0.619

Appendix

Table 10: F1-Score by dataset and over-sampling method, averaged over augmentation levels. The highest performance per dataset is in bold.

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When Does Synthetic Data Augmentation Improve Score-Based Imbalanced Classification?

Zhengchi Ma, Pengfei Lyu, Anru R. Zhang

Department of Electrical & Computer Engineering, Duke University · Department of Biostatistics & Bioinformatics, Duke University · Department of Biostatistics & Bioinformatics and Department of Computer Science, Duke University

Class-Imbalanced Learning Synthetic Data Augmentation

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Synthetic data augmentation is widely used to mitigate class imbalance, but its theoretical effects on score-based classification remain poorly understood. This paper develops a framework for characterizing when synthetic minority augmentation can improve threshold-integrated and threshold-optimized metrics, including AUROC, AUPRC, best-threshold balanced accuracy, and best-threshold

\F_1

score. We separate the effect of augmentation into two components: a change in effective class weighting and a discrepancy between the synthetic and true minority distributions. Under well-specified score models, the raw estimator already targets the likelihood-ratio ordering, which is population-optimal for the metrics considered. Consequently, augmentation cannot provide a fundamental population-level improvement beyond possible finite-sample variance reduction, and may introduce additional bias through synthetic distributional error. We further establish minimax lower bounds showing that the raw estimator already achieves the optimal metric-regret rate in the well-specified regime. Under misspecification, however, augmentation can play a qualitatively different role: by changing the effective class balance, it can alter the restricted-class projection and correct ranking errors induced by the raw imbalanced objective. We provide explicit improvement bounds quantifying the roles of approximation error, finite-sample estimation error, and synthetic distributional error. Simulation studies corroborate the theory, demonstrating limited gains under well-specification and nontrivial but nonmonotone improvements under misspecification.

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