Model-agnostic Mitigation Strategies of Data Imbalance for Regression

Andreas Rauh; Jelke Wibbeke; Sebastian Rohjans

REVIEW 3 major objections 8 minor 1 cited by

Model-agnostic Mitigation Strategies of Data Imbalance for Regression

T0 review · 3 major / 8 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper claims that crbSMOGN with density-ratio relevance reduces error on rare target values in regression better than existing imbalance strategies, and that a mean-based ensemble of mitigated and unmitigated models recovers…

desk verdict A solid, clearly-described benchmark of imbalanced-regression strategies whose headline claim that crbSMOGN is best for rare samples rests on a single train/test split per dataset, so the central comparison needs re-validation before it can be trusted. read the letter →

arxiv 2506.01486 v2 pith:XMOT5WPA submitted 2025-06-02 cs.LG

Jelke Wibbeke , Sebastian Rohjans , Andreas Rauh This is my paper · ORCID

classification cs.LG

keywords imbalancedregressionrelevancefunctiondensity-ratioresamplingcost-sensitivelearningneuralnetworksensemblemethodsrareeventprediction

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to settle how to mitigate data imbalance in regression without sacrificing overall accuracy. It argues that existing approaches either ignore the domain-specific importance of target values or damage performance on frequent samples. It introduces two relevance functions that compare the empirical density of the target variable with a domain relevance density, and two sampling methods built on them. On 10 synthetic and 42 real-world datasets, with multilayer perceptrons, XGBoost, and Random Forests, the authors find that crbSMOGN with density-ratio relevance gives the largest error reduction for very rare samples, and that a mean-based ensemble of a mitigated and an unmitigated model removes most of the frequent-sample degradation. If right, this gives practitioners a default strategy for rare-event regression and a simple fix for the trade-off.

What carries the argument

The load-bearing object is density-ratio relevance, defined as $\Lambda_{\mathrm{ratio}}(y_i) = f_x(y_i)/f_r(y_i)$, the ratio of the empirical density of the target value to the domain relevance density, inverted to a weight $w(y_i) = 1/\Lambda_{\mathrm{ratio}}(y_i)$ so that under-represented samples get high relevance. Carrying that signal is crbSMOGN, a continuous ratio-based SMOGN sampling method that over-samples each sample in proportion to its ratio relevance, uses a discretization-bounded search for interpolation partners, and falls back to Gaussian noise when no similar neighbor exists; it needs no user-set relevance threshold or sample count. The third piece is the mean-based ensemble, which averages the predictions of a model trained with mitigation and one trained without, thereby preserving rare-sample gains while canceling most frequent-sample degradation.

What would settle it

Repeat the real-world benchmark drawing several independent train/test splits per dataset and averaging the very-rare-bin error over splits; if crbSMOGN no longer beats the next-best strategies on most datasets, the reported advantage is an artifact of the chosen split.

Watch

Extended reading notes

Core claim

The central claim is that treating imbalance as the ratio between the empirical distribution of the target variable and a domain relevance distribution yields a better sampling signal than density alone. Concretely, the paper claims that crbSMOGN—a continuous, threshold-free variant of SMOGN that over-samples in proportion to a ratio-based relevance—combined with the new density-ratio relevance function, is by far the best mitigation strategy for reducing error on very rare samples when the model is a multilayer perceptron. In the real-world benchmark it produces the most significant wins in the rare bins, and the effect is smaller for XGBoost and Random Forest, which are harder to influence by resampling. The paper also claims that every mitigation strategy that helps rare samples hurts frequent ones, and that averaging a mitigated model with an unmitigated one avoids most of that loss.

Load-bearing premise

The finding rests on the assumption that the single train/test split with the lowest mean imbalance ratio, chosen from 100 random splits for each dataset, is representative enough that 50 training repetitions on that one split can stand in for variation across splits.

Editorial extensions

If this is right

For MLP models, crbSMOGN with density-ratio relevance is the best tested way to lower error on very rare target values, at only a moderate cost on frequent values.
Under-sampling generally hurts MLP performance, so over-sampling alone is the recommended configuration for neural networks.
A mean-based ensemble of a mitigated and an unmitigated model largely cancels the frequent-sample degradation while keeping most of the rare-sample improvement.
Sampling-based strategies are more effective than cost-sensitive weighting for MLP and Random Forest models, while cost-sensitive weighting works better for XGBoost.
The choice of mitigation method matters more than the choice of relevance function, and the simple WERCS method becomes competitive when paired with density-distance relevance.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Because density-ratio relevance is anchored at $w=1$ for balanced samples, the same crbSMOGN machinery could accept a non-uniform, expert-defined domain relevance distribution without changing the algorithm; the paper mentions this only as future work.
The evaluation uses a single train/test split per dataset, so the reported advantage of crbSMOGN may partly reflect split luck; a multi-split study would give a more reliable estimate of the effect.
Since under-sampling lowers the mean imbalance ratio but hurts MLP performance, the mIR alone is not a reliable predictor of which strategy will help a given model; separating data imbalance from model error imbalance would be a useful next step.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Two things you should know. First, this is a serious, clearly written empirical study: 10 synthetic and 42 real datasets, three model families, 47 mitigation-strategy combinations, and code. The methods are specified in enough detail to reimplement, and the paper is honest about several limitations. Second, the headline result—crbSMOGN with density-ratio relevance is "by far the best" for rare samples—is not yet supported, because the evaluation uses a single selected train/test split per dataset. All 50 model repetitions and all Wilcoxon tests come from that same split, so the tests measure seed noise, not split variability. That is a load-bearing flaw for the generalization claim, and the paper's discussion does not flag it.

What is new: density-ratio relevance is essentially the inverse density ratio (standard importance weighting), and density-distance is a scaled difference of densities; both generalize existing KDE-based relevance. cSMOGN and crbSMOGN are reasonable variants of SMOGN/WSMOTER with discretized neighbor search. The real contribution is the broad head-to-head comparison and the simple mean-based ensemble, which convincingly recovers frequent-sample performance. The paper also ships code, which I value.

Soft spots: the single-split protocol is the main one. The isolation-forest outlier removal (threshold 0.8) is applied before splitting and can delete the very rare target values the paper aims to study; the paper doesn't mention this. Also, with uniform domain relevance, the new relevance functions reduce to existing ones plus a midpoint shift, so their practical advantage in this benchmark is small—the paper admits this, but the abstract's framing overstates it. The finding that under-sampling generally hurts is a useful negative result. The density-ratio relevance is unbounded, which limits it to crbSMOGN; that is fine but narrow.

Overall: solid empirical work, modest novelty, honest discussion. The central ranking needs re-validation with multiple splits or a proper resampling scheme before I would trust it. I'd send it to peer review with a request for that re-analysis. For your own work, the ensemble recipe is worth remembering; the specific "best method" claim is not yet citable.

Referee Report

3 major / 8 minor

Summary. The paper addresses imbalanced regression by separating the problem into relevance functions and mitigation methods. It proposes two new relevance functions (density-distance and density-ratio) and two new sampling methods (cSMOGN and crbSMOGN), and evaluates combinations of relevance functions and mitigation methods on 10 synthetic and 42 real-world datasets with MLP, XGBoost, and Random Forest models. The central claim, stated in the abstract and in Section 4.2.3, is that crbSMOGN with density-ratio relevance is the best strategy for reducing error on (very) rare samples, particularly for MLP models, and that a mean-based ensemble of a mitigated and an unmitigated model avoids the frequent-sample degradation.

Significance. If the central claim holds, the paper makes a useful practical contribution: it systematizes the taxonomy of relevance functions and mitigation methods, introduces interpretable relevance functions that can incorporate domain preference, provides two new resampling algorithms with pseudocode and public code, and reports a broad benchmark across many datasets and three model families. The ensemble idea is simple and plausibly useful, and the paper is honest about several limitations, including the difficulty of predicting when a mitigation strategy will help and the similarity of density-distance relevance to existing methods under a uniform domain distribution. The main strength is therefore empirical breadth plus accessible methodology; the main weakness is that the headline superiority claim rests on a statistical protocol that does not sample the split distribution.

major comments (3)

[Sec. 4.2] The central comparison uses a single train/test split per dataset. The text states: 'Only the most similar (lowest mIR) split is kept and used for model training.' All 50 model repetitions, and hence all Wilcoxon signed-rank populations formed 'from the mean errors of 50 modeling repetitions per dataset and bin', are obtained on that same split. These 50 values are pseudo-replicates: they measure variation over model initializations only, not over data splits. Consequently, the per-dataset win counts and the normalized bin errors in Figs. 8-11 do not sample the split distribution, and the claim that crbSMOGN 'by far' outperforms other methods may be an artifact of the chosen split. The paper should either repeat the evaluation over multiple splits (for example, several low-mIR splits) and treat split as a random factor, or substantially temper the generalization claim.
[Sec. 4.2 / Appendix A] Before splitting, 'all datasets are cleaned of outliers using an isolation forest outlier detection' with a probability threshold of 0.8. This pre-processing can delete the extreme target values that the mitigation strategies are designed to predict, and it changes the composition of the 'very rare' bin for every method and dataset. The paper does not report how many samples are removed per dataset, nor whether the removal disproportionately affects the tails of the target distribution. The robustness of the crbSMOGN advantage should be checked without outlier removal, or at least the number and location of removed samples should be documented and discussed.
[Sec. 4.2] The statistical reporting is not sufficient to support the strength of the headline claim. The Wilcoxon tests are applied per bin to 50 correlated repetitions from one split, and then the number of significant datasets is used as a summary. This procedure does not control for multiple comparisons across the 47 mitigation strategies and five bins, and it does not provide a single test of whether crbSMOGN differs from the second-best method across datasets. In addition, Fig. 9 shows that other methods are competitive in terms of significant wins, so the 'by far the best' wording in Sec. 4.2.3 is stronger than the displayed evidence. Reporting effect sizes, confidence intervals for normalized bin errors, and a proper paired comparison across datasets would make the claim more credible.

minor comments (8)

[Abstract] The abstract contains the typo 'asses' for 'assess'; this should be corrected.
[Sec. 3.1.1] The phrase 'very marked trails' should be 'very marked tails', since the intended meaning is distribution tails.
[Sec. 3.2.8 / Sec. 3.2.9] The phrase 'bare similarity' should be 'bear similarity' in both cSMOGN and crbSMOGN descriptions.
[Sec. 3.3] Equation reference 'Ep. 16' should be 'Eq. (16)'.
[Sec. 3.2.9] The bulleted algorithm description has two items labeled '4b'; the second should be '4c'.
[Sec. 4.2.4 / Fig. 10] The caption says 'different different ensemble-formation techniques'; one 'different' should be removed.
[Appendix B, Table 5] The Friedman3 dataset is described as using 'make_friedman2'; this should be 'make_friedman3'.
[Appendix B, Table 4] The dataset name 'mortage' should be 'mortgage'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the central performance claims are empirical held-out evaluations with fixed hyperparameters.

full rationale

The paper's central claim — that crbSMOGN with density-ratio relevance best reduces error on rare samples for MLPs — is an empirical benchmark result, not a quantity derived from a fitted constant. Relevance values are computed from training-target density with a uniform domain relevance and are not calibrated to test data; hyperparameters are fixed before evaluation as listed in Appendix A. The split-selection protocol uses the authors' own mIR metric from Wibbeke et al. (2025), but that metric is externally published with available code and is used only to choose a train/test split, not to construct the bin errors or the Wilcoxon populations; the measured bin errors are independent of the mIR value. The self-citations to Wibbeke et al. (2025) and Kowatsch et al. (2024) motivate the two-distribution formalism, but the performance comparison would stand even if any inverse-density relevance were used; no uniqueness theorem or prior result is invoked to forbid alternatives. The new density-ratio relevance with uniform f_r reduces to an inverse empirical density, a known construction, and the paper's own Discussion (Sec. 5) concedes that density-distance, KDE, and DenseWeight differ only slightly under uniform preference; the advantage of crbSMOGN is attributed to the sampling scheme rather than to a new derivation. The acknowledged limitations (Sec. 5: 'no reliable statements can be made about which properties a dataset or a modeling task must fulfill') and the single-split, 50-repeat protocol are statistical-validity concerns, not circularity: the 'prediction' is a measured held-out bin error, not an input recycled as output. Therefore no circular step is exhibited.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central contribution is empirical; the main load-bearing choices are the evaluation protocol (single selected split, outlier removal, fixed hyperparameters) rather than free parameters fitted to the target result. No new physical or formal entities are introduced.

free parameters (6)

isolation forest outlier probability threshold = 0.8
Samples with outlier probability >= 0.8 are removed from every dataset. In skewed targets this may delete the extreme rare values the study is meant to evaluate. No per-dataset tuning or sensitivity analysis is reported.
number of bins for discretization (cSMOGN, crbSMOGN) = 10
Controls the neighborhood search space for over-sampling. Fixed across datasets without tuning.
allowed bin deviation delta_b (cSMOGN, crbSMOGN) = 1
Limits how far bin-wise a second seed sample can be. Fixed across datasets.
Gaussian noise level delta_n = 0.01 * std
Magnitude of noise added when no interpolation seed is found in SMOGN, cSMOGN and crbSMOGN. Fixed across datasets.
SMOGN relevance threshold = 0.8
Samples above 0.8 are over-sampled, below are under-sampled; this threshold changes which samples are treated as rare. Fixed for all datasets.
number of random splits scored for mIR selection = 100
The paper keeps only the split with the lowest mean imbalance ratio. This is a choice about the evaluation protocol, not the model, but it directly affects the reported ranking.

assumptions (5)

domain assumption The domain relevance distribution f_r is uniform in all experiments.
The new relevance functions require an explicit domain relevance density, but the paper sets it uniform ('we thus assume that there is no domain preference', Section 4) to stay comparable with other methods. This limits the evaluation to uniform-importance settings.
domain assumption Kernel density estimates use Silverman's rule of thumb for bandwidth.
All density-based relevance functions rely on KDE with Silverman bandwidth (Section 4), which is known to over-smooth non-normal distributions. The paper acknowledges this and keeps it for comparability.
domain assumption The isolation forest outlier removal does not discard the rare samples that the study targets.
All datasets are cleaned with an isolation forest at threshold 0.8 (Section 4.2). If extreme rare target values are flagged as outliers, the very rare bins would be artificially emptied or altered, biasing the comparison.
ad hoc to paper The lowest-mIR split is representative of typical train/test conditions.
Choosing the split with the lowest mean imbalance ratio among 100 candidates is an ad hoc protocol; without justification, results may be conditional on an unusually well-matched split.
standard math Standard mathematical and ML background assumptions (kNN distances, SMOTE interpolation, etc.) hold.
These are standard tools in the field and are used as building blocks; no novel mathematical claims are made.

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Cite this review

Pith. "Pith review of Model-agnostic Mitigation Strategies of Data Imbalance for Regression." pith.science (2026). https://pith.science/paper/XMOT5WPA

@misc{pith2026250601486,
  author       = {Pith},
  title        = {Pith review of: Model-agnostic Mitigation Strategies of Data Imbalance for Regression},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XMOT5WPA}},
  note         = {Machine review of arXiv:2506.01486}
}

read the original abstract

Data imbalance persists as a pervasive challenge in regression tasks, introducing bias in model performance and undermining predictive reliability. This is particularly detrimental in applications aimed at predicting rare events that fall outside of the domain of the bulk of the training data. In this study, we review the current state-of-the-art regarding sampling-based methods and cost-sensitive learning. Additionally, we propose novel approaches to mitigate model bias. To better assess the importance of data, we introduce the density-distance and density-ratio relevance functions, which effectively integrate empirical frequency of data with domain-specific preferences, offering enhanced interpretability for end-users. Furthermore, we present advanced mitigation techniques (cSMOGN and crbSMOGN), which build upon and improve existing sampling methods. In a quantitative evaluation, we benchmark state-of-the-art methods on 10 synthetic and 42 real-world datasets, using neural networks, XGBoosting trees and Random Forest models. Our analysis shows that while most strategies improve performance on rare samples, they degrade it on frequent ones. The trade-off becomes larger the more the performance on rare samples is increased. However, to reduce this effect we demonstrate that constructing an ensemble of models -- one trained with imbalance mitigation and another without -- can be used. The key findings underscore the superior performance of our novel crbSMOGN sampling technique with the density-ratio relevance function for neural networks, outperforming state-of-the-art methods.

Figures

Figures reproduced from arXiv: 2506.01486 by the authors.

**Figure 2.** Distribution of the target variable (electrical energy) of the combined-cycle-power-plant dataset (see Appendix [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Comparison of the effect of different data imbalance mitigation methods on the target variable of the synthetic [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗

Figures from the paper (8 more)

**Figure 4.** Figure 4: Exemplary bin-error-plot. The model error for each sample frequency bin is normalized and averaged over all [PITH_FULL_IMAGE:figures/full_fig_p019_4.png]

**Figure 5.** Figure 5: Exemplary bin-win-plot. Number of datasets won and lost by models employing different mitigation strategies [PITH_FULL_IMAGE:figures/full_fig_p019_5.png]

**Figure 6.** Figure 6: Performance evaluation of the three tested model types without any imbalance mitigation methods over 42 [PITH_FULL_IMAGE:figures/full_fig_p020_6.png]

**Figure 7.** Figure 7: Bin-error-plot of the synthetic datasets. Left: representation of all tested combinations of relevance function, [PITH_FULL_IMAGE:figures/full_fig_p021_7.png]

**Figure 8.** Figure 8: Bin-error-plot of the real world datasets. Left: representation of all tested combinations of relevance function, [PITH_FULL_IMAGE:figures/full_fig_p023_8.png]

**Figure 9.** Figure 9: Bin-win-plots for the three model types comparing model trained with mitigation strategy to models trained [PITH_FULL_IMAGE:figures/full_fig_p024_9.png]

**Figure 10.** Figure 10: Bin-win-plots for different different mitigation strategies comparing ensemble-formation techniques [PITH_FULL_IMAGE:figures/full_fig_p025_10.png]

**Figure 11.** Figure 11: Bin-error-plot of the mean-based ensembles compared to single models using real world datasets. [PITH_FULL_IMAGE:figures/full_fig_p026_11.png]

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

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Imbalance in Regression Datasets

Daniel Kowatsch, Nicolas M Müller, Kilian Tscharke, Philip Sperl, and Konstantin Bötinger. Imbalance in regression datasets.arXiv preprint arXiv:2402.11963,

work page Pith review arXiv

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