CARTGen-IR: Synthetic Tabular Data Generation for Imbalanced Regression

Ant\'onio Pedro Pinheiro; Rita P. Ribeiro

REVIEW 3 major objections 5 minor 29 references

CARTGen-IR: Synthetic Tabular Data Generation for Imbalanced Regression

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper introduces CARTGen-IR, a threshold-free CART-based synthetic sampler for imbalanced regression that weights rare target values, resamples them, and generates new rows column-by-column from tree leaves; the reported experiments…

desk verdict Solid empirical contribution but the 'generally superior' claim overreaches due to selective configuration reporting and a one-vs-one Bayesian test. read the letter →

arxiv 2506.02811 v2 pith:264DXOCG submitted 2025-06-03 cs.LG

António Pedro Pinheiro , Rita P. Ribeiro This is my paper

classification cs.LG

keywords imbalancedregressionsyntheticdatagenerationtabularCARToversamplingextremevaluepredictionDenseWeightrelevancefunction

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

The paper introduces CARTGen-IR, a way to generate synthetic rows for imbalanced regression without cutting the continuous target into arbitrary bins or thresholds. It first gives each case a rarity weight, resamples the rare cases, then uses decision trees to generate each column conditionally on the previous columns, producing new rows that stay close to the observed data distribution. The authors' claim is that this threshold-free, tree-based sampler is competitive with or generally superior to both classical resamplers and deep generative models on extreme-value prediction benchmarks, while running far faster and remaining interpretable.

What carries the argument

The load-bearing object is the sequential, attribute-wise CART generator: for each column, a decision tree is fit with that column as target and only earlier columns as predictors; a new synthetic row begins with the first column drawn from the whole pool (root node) and each later column by routing through the tree to a leaf and sampling a value from the leaf's members, using a Gaussian kernel density estimate for continuous attributes. Rarity weighting (DenseWeight or relevance function, raised to an exponent and normalized) selects which original rows to resample, with an optional jitter on duplicates. The trees are fit once on the resampled data and reused for every synthetic case, so generation is transparent and does not depend on the synthetic rows already produced.

What would settle it

Permute the order of the feature columns on a dataset with known strong interactions, run CARTGen-IR with fixed hyperparameters, and measure SERA; if some orders degrade sharply or the advantage over plain resampling disappears, the sequential column-order assumption is doing the work.

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Extended reading notes

Core claim

The paper's central claim is that a decision-tree generator, CARTGen-IR, is a strong data-level method for imbalanced regression. It weights each target value by rarity (DenseWeight or relevance), resamples the original data so rare rows dominate, then builds a separate CART for each feature using only earlier features as predictors and draws new values from leaf nodes, smoothing continuous variables with a Gaussian kernel. In experiments across 15 datasets, 56 preprocessing configurations, and three regressors, the method matches or beats leading resamplers such as WSMOTER, KNNOR-REG, and G-SMOTER on imbalanced-regression metrics, and is about 131 times faster on average than the deep generative models tested, while avoiding arbitrary target thresholds.

Load-bearing premise

The method assumes that generating features in a fixed column order, with each feature depending only on earlier features, captures the real joint distribution; if that order hides important interactions, the synthetic rows can be unrealistic even when the resampling weights are right.

Editorial extensions

If this is right

Because CARTGen-IR needs no user threshold on the target, the same resampling recipe applies whether the rare values are high, low, or both, without redefining a cutoff per dataset.
The method can be inserted into standard preprocessing pipelines for regressors such as Random Forest, SVR, and XGBoost, improving imbalanced-regression metrics (SERA, RW-RMSE) on rare cases while keeping RMSE comparable.
Its execution time is orders of magnitude below deep generative models (about 131 times faster on average in the reported experiments), making it practical for larger tabular data.
Its white-box tree structure allows a practitioner to inspect exactly which leaf nodes produced the synthetic rows, supporting auditability that GAN, VAE, and diffusion approaches lack.

Reading between the lines

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

Because the generation is sequential in a fixed column order, the choice of column order likely matters; the authors report no permutation sensitivity analysis, so a prudent user would permute columns and check whether the reported advantage holds.
The rarity-weighting step is plug-in, so the same CART generation machinery could be combined with weights from domain knowledge or cost-sensitive objectives; this extension is implicit in the framework and untested.
The benchmark datasets mostly define rarity through extreme tails; whether the method also helps for rare mid-range intervals (a plateau in the target density) is an open question the authors themselves flag as future work.

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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

Couple of things to know. CARTGen-IR is a threshold-free, CART-based synthetic data generator for imbalanced regression. The method is an adaptation of existing pieces—DenseWeight/relevance weighting plus sequential attribute-wise CART generation from Reiter and from Panagiotou et al.—but combining them for imbalanced regression is new, and the paper does a thorough empirical job. It has a clear algorithm, handles mixed types and missing values, and ships code and results.

What it does well: 15 datasets, three learners, repeated stratified nested CV, Wilcoxon significance tests, a Bayesian signed-rank comparison, runtime analysis. The sensitivity analysis of alpha, eta, delta, rho is genuinely useful. The transparency angle is real: tree-based generation is far more interpretable than GANs and diffusion models.

Soft spots: the headline 'generally superior' claim overreaches. Figure 3 shows only the six best CARTGen-IR configurations out of 16, while showing all competitor configurations; that selection is acknowledged but makes the win/loss comparison unfair. The Bayesian test supporting the superiority claim is run only against WSMOTER, after the fact, on the selected variants. The paper would be more honest saying CARTGen-IR is competitive with, and often better than, the tested alternatives under the configurations tested. DIRVAE and IRGAN are missing because code is unavailable—fine, but then the paper shouldn't imply it beats all state-of-the-art methods.

The ordering concern: sequential generation with a fixed column order is an autoregressive factorization. Any order defines a valid joint, but the estimated conditionals may not match the data distribution well with finite samples. The paper doesn't test sensitivity to column order. That's a real omission but minor—it doesn't invalidate the method, and the authors flag interactions as future work.

Bottom line: a solid empirical paper for the imbalanced regression subfield. It deserves a serious referee and likely a major-revision outcome if the authors are asked to show all configurations or justify the selection, and add an ordering sensitivity check. The core contribution—a fast, interpretable, threshold-free alternative to deep generative models—holds up. Recommendation: send to peer review.

Referee Report

3 major / 5 minor

Summary. The manuscript proposes CARTGen-IR, a data-level synthetic data generation method for imbalanced regression. Rarity weights are computed via DenseWeight or a relevance function, the dataset is resampled with replacement according to those weights, and synthetic rows are generated by fitting one CART per attribute in a fixed order and sampling from leaf nodes, with Gaussian KDE smoothing for continuous features. The method is evaluated on 15 benchmark datasets with three learners (RF, SVR, XGBoost) and compared against classical resamplers and deep generative models under repeated 2x5-fold cross-validation, using RMSE, RW-RMSE, and SERA, plus a runtime comparison. The paper claims that CARTGen-IR is generally superior to state-of-the-art methods and offers a strong balance between efficiency and predictive performance.

Significance. If the empirical claims were fully supported, this would be a useful contribution: a threshold-free, interpretable, and computationally efficient data-level method for imbalanced regression that is competitive with deep generative models. The experimental infrastructure is substantial, with 15 datasets, three learners, nested cross-validation, statistical tests, and a runtime analysis, and the authors make code and results available. However, the headline comparison is weakened by post-hoc selection of CARTGen-IR configurations and by internal inconsistencies in the reported configuration counts, so the significance of the claimed superiority cannot be assessed as the manuscript stands.

major comments (3)

[§4.2, Fig. 3] Figure 3 reports only the six best-performing CARTGen-IR configurations out of 16 tested, while all competitor configurations are shown; no selection rule is stated, and the six appear to have been chosen after inspecting results. This post-hoc selection biases the win/loss analysis in favor of CARTGen-IR and does not support the sentence 'Overall, the analysis suggests that CARTGen-IR is generally the superior method.' The subsequent Bayesian signed-rank test is also post-hoc: it compares CARTGen-IR with WSMOTER only because both performed well in earlier tests, uses a ROPE of [-1%, 1%], and applies no correction for the many configurations and baselines examined. Please report results for all configurations (or use a pre-specified inner-CV selection rule) and temper the superiority claim accordingly.
[§3, Algorithm 1] The sequential attribute-wise generation is an autoregressive factorization with a fixed column order: the first attribute is sampled from its marginal pool, and every later attribute is conditioned only on previously generated attributes. This is a strong structural assumption about the joint distribution; if the first attribute is high-cardinality or strongly interacting, synthetic rows can be unrealistic even when rarity weights are correct. The paper acknowledges this indirectly in the conclusion ('alternative methods can be employed to capitalize on the interactions between features'), but the abstract's claim of generating 'realistic tabular samples across heterogeneous features and non-linear interactions' is load-bearing. No sensitivity analysis over attribute ordering is reported; please add one (e.g., random or permuted orders with distributional fidelity or downstream performance checks) or restrict the generality claims.
[§4.1, Table 2 and §4.2] The configuration counts are internally inconsistent. Table 2 defines 2x3x2x2 = 24 CARTGen-IR configurations (rho x alpha x eta x delta), while the text and Figure 3 say '16 tested' and 'six best-performing configurations (out of 16 tested).' The total of '56 resampling configurations' also does not match the sum of Table 2 under either count (53 with 16 CARTGen-IR configurations, 61 with 24). Please correct the counts and clarify whether some hyperparameter combinations were excluded and why; this matters because the reported number of configurations is part of the post-hoc selection issue.

minor comments (5)

[§3, FitCARTModels description] The text says the trees are 'derived solely from the original data,' but Algorithm 1 calls FitCARTModels on the resampled dataset (Xnew, Ynew), which can contain duplicate rows and is not the original data; please reconcile this wording with the algorithm.
[§4.3] The statement that CARTGen-IR 'ranks the highest overall' appears inconsistent with §4.2's statement that WSMOTER is 'the most consistent performer' and CARTGen-IR 'ranks fourth in overall consistency'; please rephrase to avoid contradiction.
[§4.2, Fig. 6] The claim that CARTGen-IR is 'the second fastest' should be stated more precisely as 'second fastest among synthetic-data generators,' since RU, RO, and WERCS are sampling-only methods and are faster by construction.
[§4.2, Fig. 5] The sensitivity analysis in Figure 5 uses an unnamed 'representative regression dataset'; please identify the dataset explicitly so the reader can judge the generality of those results.
[§4.2] The code repository is mentioned as 'SynthTabularDataGeneration-IR' but no URL is provided; please include a working link or persistent identifier.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: CARTGen-IR's claims are empirical comparisons; the synthetic generation procedure is defined independently of the evaluation metrics, and the only author-related citation (the relevance function [22]) is an externally published, non-exclusive input.

full rationale

CARTGen-IR is an empirical method paper, not a derivation chain, so there is no equation-level reduction of a predicted quantity to an input. The synthetic generation procedure is defined independently: rarity weights come from DenseWeight [24] or the relevance function [22], and the CART-based sequential attribute generation is described procedurally in Section 3 and Algorithm 1. The evaluation metrics SERA and RW-RMSE are relevance-weighted, but they are applied uniformly to all compared strategies, so favoring a method that also uses a relevance function is not a by-construction equivalence; the paper explicitly tests both weighting schemes, including the non-relevance DenseWeight alternative. The sequential attribute-wise CART factorization is a fixed-order conditional model, but that is a modeling assumption and a potential limitation, not a circularity: the paper does not define the target result in terms of that ordering, and it even acknowledges in the conclusion that alternative learners and feature-interaction mechanisms could be explored. The post-hoc reporting of the six best CARTGen-IR configurations out of 16 tested is a selection-bias concern that can inflate apparent performance, but it is not a fitted parameter renamed as a prediction, and it does not reduce the comparative claim to an identity. The only self-citation of note is [22], co-authored by one of the current authors and used for both the relevance weighting scheme and the SERA metric; however, it is an established, externally falsifiable method, the paper also implements DenseWeight, and the central claim of competitiveness is an empirical outcome rather than a consequence implied by the citation. Overall, no circular step is identifiable by the paper's own equations or definitions.

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

The central claim rests on the validity of the sequential CART factorization, the usefulness of the external rarity estimates, and several hand-chosen hyperparameters. No new physical or conceptual entities are introduced.

free parameters (6)

Rarity exponent alpha = 1.0, 1.5, 2.0
Controls how strongly rarity weights are exaggerated before resampling; selected from a search space refined by preliminary empirical analysis (Section 4.1), and the best values depend on the weighting scheme (Section 4.2).
Sampling proportion eta = 0.5, 0.75
Fraction of synthetic cases generated relative to the original dataset size; both values were tested and little influence on results is reported (Section 4.2).
Noise level delta = 0.001, 0
Gaussian jitter added to duplicate numeric features to reduce overfitting; the stronger CARTGen-IR variants introduced noise (Section 4.2).
Weight scheme rho = denseweight, relevance
Choice of rarity estimation mechanism; relevance consistently led to better performance than denseweight in the sensitivity analysis (Section 4.2).
Resampled case count Nre = floor(N/5) = floor(eta * |Y| / 5)
Fixed fraction of synthetic cases used as the resampling base, citing prior SMOTE and ADASYN practice [12,13]; this value is arbitrary and not tuned.
Attribute ordering = natural column order
Sequential attribute-wise generation uses the given column order, with each variable predicted only by preceding variables. No ordering selection or sensitivity analysis is reported.

assumptions (5)

standard math CART leaf sampling approximates the conditional distribution of the target attribute given the splitting variables.
Section 3, FitCARTModels and GenSynthetic: values are randomly drawn from members of the selected terminal node, with kernel smoothing added for continuous features.
ad hoc to paper Sequential factorization of the joint distribution by a fixed variable order is valid for generating realistic mixed-type tabular data.
Section 3 states that 'a CART model is iteratively fitted for each attribute using the remaining, previous attributes as predictors'; no theoretical or empirical validation of the ordering assumption is provided.
domain assumption DenseWeight and the relevance function correctly identify rare and relevant target regions.
Section 3 RarityWeights uses DenseWeight [24] or relevance [22] as the only rarity estimators; the method's success depends on these estimates being meaningful for the problem.
domain assumption Resampling with replacement weighted by rarity, followed by fitting CART on the resampled set, concentrates synthetic samples in rare regions without distorting feature relationships.
Algorithm 1 samples with weights w and then calls FitCARTModels on the resampled data; if resampling distorts conditional dependencies, generated samples inherit the distortion.
ad hoc to paper Gaussian jitter on duplicate rows improves generalization without materially changing the data distribution.
Algorithm 1 applies JitterDuplicates when delta > 0; the noise magnitude is hand-chosen (0.001) and its effect is asymmetric across weighting schemes (Section 4.2).

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Cite this review

Pith. "Pith review of CARTGen-IR: Synthetic Tabular Data Generation for Imbalanced Regression." pith.science (2026). https://pith.science/paper/264DXOCG

@misc{pith2026250602811,
  author       = {Pith},
  title        = {Pith review of: CARTGen-IR: Synthetic Tabular Data Generation for Imbalanced Regression},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/264DXOCG}},
  note         = {Machine review of arXiv:2506.02811}
}

read the original abstract

Handling imbalanced target distributions in regression poses a persistent challenge, as the underrepresentation of relevant target values can significantly hinder model performance. Existing data-level solutions often adapt classification-oriented techniques, introducing arbitrary thresholds over the continuous target and leading to artificial and potentially misleading problem formulations. Deep generative models offer flexible sample synthesis but are computationally intensive and difficult to interpret. We propose a CART-based synthetic sampling method specifically designed for imbalanced regression on tabular data. The method integrates relevance- and density-guided sampling to address sparse target regions without thresholding, and employs a feature-driven tree structure to generate realistic tabular samples across heterogeneous features and non-linear interactions. Experiments on benchmark datasets for extreme-value prediction show that the proposed approach is competitive with state-of-the-art resampling and generative methods while offering faster execution and greater transparency. These results highlight its potential as a scalable and interpretable data-level strategy for improving regression models in imbalanced domains.

Figures

Figures reproduced from arXiv: 2506.02811 by the authors.

**Figure 1.** CART consecutive column-wise data generation. [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗

**Figure 2.** Synthetic sample generation comparison [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

Figures from the paper (4 more)

**Figure 3.** Figure 3: Comparison of wins and losses, including significant outcomes at the 95% [PITH_FULL_IMAGE:figures/full_fig_p009_3.png]

**Figure 4.** Figure 4: Bayesian posterior ternary plots. We also conducted a hyperparameter sensitivity analysis of CARTGen-IR, examining the effects of the density scheme ρ, exponent α, sampling proportion η, and noise level δ on performance. Results were obtained using a Random Forest mode…

**Figure 5.** Figure 5: Sensitivity analysis of CARTGen-IR with respect to the density weighting [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]

**Figure 6.** Figure 6: Aggregated average runtime per data-level strategy. [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]

Discussion (0). Sign in to comment.

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