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REVIEW 4 major objections 4 minor 2 cited by

Data Augmentation with Variational Autoencoder for Imbalanced Dataset

T0 review · 4 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The paper claims that a variational autoencoder trained with an inverse-density weighted loss and generating new points by smoothed bootstrap in its latent space—the DAVID algorithm—outperforms the initial training sample and existing…

desk verdict DAVID's method is sensible and the simulation is decent, but the real-data claim rests on a metric the method is built to optimize. read the letter →

arxiv 2412.07039 v1 pith:MDZGAIT7 submitted 2024-12-09 cs.LG

Samuel Stocksieker , Denys Pommeret , Arthur Charpentier This is my paper · ORCID
classification cs.LG
keywords imbalancedregressionvariationalautoencodersmoothedbootstrapdataaugmentationsyntheticgenerationtabularbalancedlossrarevalues
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

Imbalanced regression, where a continuous target has few rare extreme values, remains under-served compared with classification. The paper proposes DAVID, which trains a variational autoencoder (VAE) with a loss that weights each observation by the inverse of the estimated density of the target, so rare values contribute more to reconstruction. Instead of sampling new latent points from each observation's inferred Gaussian, DAVID draws seeds from the latent means with a kernel-smoothed bootstrap, using each rare point's neighborhood to generate new rare values. The authors report that on simulated data and four benchmark datasets, DAVID gives lower weighted mean squared error than the initial training sample and than state-of-the-art imbalanced-regression methods such as SMOGN, SMOTE for regression, and Gaussian noise, as well as general-purpose generators like TVAE and CTGAN.

What carries the argument

The object that carries the argument is the DAVID generator: a $\beta$-VAE for regression whose target-reconstruction term is weighted by $\omega_i = 1/\hat{f}_Y(y_i)^\alpha$ (inverse empirical density of the target, estimated by kernel density with Silverman or Scott bandwidth), followed by a smoothed bootstrap over the encoder's latent means $\mu_i$. The smoothed bootstrap draws a seed $\mu_i$ with probability $\omega_i$ and adds Gaussian noise $K_{H_n}(z^* - \mu_i)$ with $H_n = \eta \cdot \mathrm{Var}(\mu)$, where $\eta$ follows Silverman's or Scott's rule of thumb. This replaces the VAE's native sampling $z_i = \mu_i + \sigma_i \varepsilon$, which is unreliable for rare values because $\sigma_i$ is poorly estimated. The smoothed bootstrap uses the neighborhood structure of the latent space, and the VAE's regularity makes that neighborhood meaningful; this is what allows the non-parametric generation of rare target values.

What would settle it

On an imbalanced-regression benchmark, train DAVID and a control that uses the same balanced-loss VAE but generates from the native per-observation Gaussians $\mathcal{N}(\mu_i, \sigma_i)$ instead of the smoothed bootstrap, with identical seeds and $\alpha$; if the control matches DAVID's wMSE, the smoothed bootstrap is not the active ingredient. Alternatively, compute the reconstruction error of DAVID's generated rare-value points through the encoder-decoder: if the error is no better than random latent draws, the generator is producing off-manifold samples.

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Extended reading notes

Core claim

The central discovery is that the failure of VAEs on imbalanced regression is not primarily a reconstruction problem but a generation problem: the per-observation latent variance $\sigma_i$ for rare values is poorly estimated and too large, so sampling from $\mathcal{N}(\mu_i, \sigma_i)$ pushes generated points off the rare-value manifold. DAVID replaces this with a joint generator $g_{z^*}(z^*|\mu) = \sum_i \omega_i K_{H_n}(z^* - \mu_i)$, a Gaussian-mixture smoothed bootstrap over the latent means $\mu_i$ with bandwidth $H_n$ from Silverman's or Scott's rule, and seed weights $\omega_i = 1/\hat{f}_Y(y_i)^\alpha$. Because the VAE's latent space is regular (continuous and complete), kernel density estimation is valid there—unlike in the original data space or in a plain autoencoder's latent space. The authors show each component matters: the balanced loss improves over the vanilla $\beta$-VAE, the smoothed bootstrap improves over natural VAE generation, and combined (kBVAEw, which is DAVID) they beat the baseline and competitors on weighted MSE.

Load-bearing premise

The method's gains depend on the VAE learning a latent space that is regular and faithful enough that kernel-smoothed neighborhoods around the latent means $\mu_i$ correspond to valid, on-manifold rare-value samples; if the VAE is poorly trained, the generated points are off-manifold and augmentation can worsen regression, as the paper itself notes.

Editorial extensions

If this is right

  • DAVID lowers weighted MSE on the four real benchmark datasets (bank8fm, abalone, boston, NO2), achieving the best mean wMSE among all compared methods.
  • Standard synthetic generators not designed for imbalanced regression (TVAE, CTGAN, CopulaGAN) degrade performance relative to the initial sample, so they should not be used for this task without adaptation.
  • Generating in the latent space of a regular VAE is more effective than generating in the original data space (kTrain) or in PCA or kernel-PCA latent spaces.
  • The balanced loss alone (BVAEw) improves over the vanilla VAE, and the smoothed bootstrap alone (kBVAE) is comparable to natural VAE generation, so the two modifications are complementary.
  • Because the method is a preprocessing step, it works with any downstream regressor, including the white-box models preferred in insurance and finance.

Reading between the lines

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

  • A testable extension is to adapt DAVID's weighting scheme to classification by replacing the continuous target density with class-frequency weights, then applying the smoothed bootstrap to generate minority-class latent samples without binning the target.
  • The success of the smoothed bootstrap suggests that VAE variance estimates are the bottleneck for rare-value generation; one could directly regularize $\sigma_i$ (e.g., shrink large variances) and test whether the gap between natural VAE generation and smoothed bootstrap closes.
  • The method's dependence on the VAE's latent regularity implies that the generator's performance can serve as a diagnostic for latent-space quality: if wMSE degrades, the encoder has likely not learned a continuous manifold.
  • Since the paper averages results over ten models via H2O AutoML, the gains are already model-averaged; a further test would isolate which base learners benefit most from DAVID augmentation.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper proposes DAVID, a data augmentation method for imbalanced regression (IR) on tabular data, which combines a β-VAE with a balanced loss and a smoothed bootstrap over the latent means. The balanced loss weights observations by the inverse of the estimated target density, and the smoothed bootstrap generates new latent points from kernel density estimates centered on the latent means, with seeds drawn according to the same inverse-density weights. The method is evaluated on one simulated dataset and four real IR benchmark datasets, comparing against several baselines and state-of-the-art methods. The authors report that DAVID outperforms the initial training sample and the competitors, especially on the real datasets where only the self-defined wMSE metric is reported.

Significance. If the reported gains hold, the method is a useful contribution to the under-studied area of imbalanced regression, offering a principled way to adapt VAEs to IR without discretizing the target variable. The paper's strengths include a clearly described algorithm, a step-by-step ablation on the simulation, the use of multiple learning algorithms via H2O AutoML, and publicly available code on GitHub. The simulation results do include standard MSE/MAE/MAPE metrics, which is commendable. However, the central claim of superiority on real datasets rests on a custom wMSE metric that is aligned with the training objective, and the real-data evaluation lacks standard error metrics and statistical significance tests. The paper also acknowledges a key limitation—the method fails if the VAE is not functioning properly—but does not provide diagnostics to delineate when it works. These gaps currently prevent full verification of the central claim.

major comments (4)
  1. [§5, Table 2] The central claim that DAVID 'gives better results than the initial training sample and the state-of-the-art approaches' is supported in Section 5 only by the self-defined wMSE, whose weights ω_i = 1/f_Y(y_i)^α (Eq. 2) coincide with the inverse-density weights used in the training loss (Eq. 1) and in the smoothed-bootstrap seed drawing (Section 3.4). Because the metric and the training objective share the same weighting, the reported wMSE improvement is partly a direct consequence of the method's design; to establish the claim, the authors should report standard MSE/MAE (as done in the simulation, Table 1) on the real datasets, ideally together with a metric that is not aligned with the training loss.
  2. [§5, Tables 2 and 1] No statistical significance testing is provided for the 10-fold comparisons. For example, bank8FM baseline wMSE is 1.87 ± 0.19 versus DAVID's 1.68 ± 0.13, and abalone 6.84 ± 0.29 versus 5.52 ± 0.22; these differences are small relative to the reported spreads, so it is unclear whether the improvement is systematic. Paired tests (e.g., Wilcoxon signed-rank across folds) or confidence intervals should be added for both tables; otherwise the 'better results' claim is not robust.
  3. [§4.2] Two state-of-the-art methods are missing from the comparison: ADASYN was removed after the authors observed poor results and high computation time, and VIR (Wang and Wang, 2024) was not compared because its code is no longer accessible. The VIR exclusion is particularly relevant because VIR is the closest existing VAE-based imbalanced regression method, and the paper's claim of outperforming state-of-the-art VAE approaches cannot be verified without it. At minimum, the authors should discuss the expected comparison and report any partial results; the ADASYN exclusion should be documented with its quantitative results in an appendix rather than reported only qualitatively.
  4. [§6, Discussion] The paper explicitly states 'the method would not work if the VAE is not functioning properly,' yet no diagnostic of VAE quality (e.g., reconstruction error on rare values, or latent-space uniformity checks) is reported for the simulations or real datasets. Since the method's validity depends on the latent space accurately reflecting the data, the empirical section should include such diagnostics or a sensitivity analysis over β_KL and α to demonstrate the regime in which DAVID is effective. This is not a fatal flaw given the acknowledgment, but it is needed to bound the method's scope.
minor comments (4)
  1. [§5, Table 2] Table 2 contains a row 'kTrain' that is not defined in the protocol list in §4.2; presumably it refers to smoothed bootstrap applied in the original data space (called CSB in Table 1), but the naming should be consistent.
  2. [§4.2, Table 1] The label 'OVAE' is used inconsistently for what should be '0VAE' (zero-KL VAE); the text and tables should use the same label.
  3. [§3.2, Eq. (1)] In Eq. (1), the weighting term is written as 'bf (Y )α', but the notation is not formally defined; it should be f̂_Y(y)^α to match Eq. (2).
  4. [§4.2 and Appendix A] The protocol text states that 70% of the data is allocated to the training set, while Appendix A specifies a 60-40% train-test split; this inconsistency should be reconciled.

Circularity Check

1 steps flagged · score 6.0 of 10

The real-data superiority claim is evaluated with the same inverse-density weights that the method is built to optimize, making the headline wMSE gain partly tautological.

  1. fitted input called prediction [Section 3.2, Eq. (1); Section 3.3, Eq. (2); Section 4.3, wMSE definition; Section 5, Table 2]
    ""we propose to weigh the observations during the training phase by the inverse of the empirical density of Y" ... L(θ, ϕ,x, y) = β_x E_q[log pθ(x|z)] − β_KL D_KL(qθ(z|x)||pθ(z)) + β_y / bf(Y)^α E_q[log pθ(y|z)] (1) ... "ω_i := 1/\hat f_Y(y_i)^α (2)" ... "Our weighted MSE wMSE(Y, Ŷ) := 1/n Σ ω_i (y_i − ŷ_i)^2 with ω_i defined as in 2" ... "DA VID ('kBV AEw') gives better results than the initial training sample and the state-of-the-art approaches.""

    The same inverse-target-density weights ω_i are fitted from the training data and then inserted into three places: the VAE objective (Eq. 1 weights the y-reconstruction by β_y / f(Y)^α), the seed drawing of the smoothed bootstrap (Sec. 3.3: "the first step is represented by the drawing weight ω_i"), and the evaluation metric wMSE (Sec. 4.3, using "ω_i defined as in 2"). Thus the headline real-data result in Table 2 is a comparison on the very metric that DAVID is constructed to improve: rebalancing the loss and the generated sample by 1/f_Y^α will, other things equal, reduce that same 1/f_Y^α-weighted test error.

full rationale

The paper's derivation chain is otherwise self-contained: the VAE loss, the smoothed-bootstrap generator, and the DAVID algorithm are defined independently of the empirical claim, and no load-bearing conclusion is imported from the authors' earlier work (Stocksieker et al. 2023 appears only as related work, not as a justification of the method). The Discussion also candidly limits the method to cases where the VAE works, saying "the method would not work if the VAE is not functioning properly," which is an external modeling assumption rather than a circular step. The circularity concern is specifically evaluative: Eq. (2) defines ω_i from the inverse density of the target, Eq. (1) uses those weights in the training loss, the smoothed bootstrap uses them for seed drawing, and Section 4.3 defines wMSE with "ω_i defined as in 2." Since Table 2 reports only wMSE for the real datasets, the central claim that "DA VID ... gives better results than the initial training sample and the state-of-the-art approaches" is measured with a metric that the method is explicitly designed to optimize. This makes the headline real-data gain partly tautological, though not fully forced because the downstream regressors are not directly minimizing wMSE. The simulation results with standard MSE/MAE provide some independent support, so the overall circularity is partial rather than total.

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

The method's contribution rests on standard VAE and KDE machinery plus a small set of hand-set hyperparameters. No new physical or mathematical entities are invented. The key domain assumption is that the VAE's latent space is regular enough for the smoothed bootstrap to generate valid rare samples, which the paper itself flags as fragile.

free parameters (5)
  • alpha (exponent for inverse density weights) = 1
    Controls the strength of rebalancing in weights omega_i = 1/f_hat(y)^alpha (Eq 2). Set to 1 in all experiments, which makes the resampled target distribution uniform. No sensitivity analysis is reported.
  • beta_y (weight of target reconstruction in loss) = 10
    Multiplier for the Y reconstruction term in the VAE loss (Eq 1). Chosen as approximately the number of covariates. Hand-set, not tuned.
  • beta_KL (weight of KL divergence) = 1e-6
    Penalty on the KL term in the VAE loss. Set to a small value to avoid posterior collapse, as noted in Appendix A. Hand-set.
  • noise scaling parameter for smoothed bootstrap = 0.1
    Multiplicative parameter applied to the smoothing matrix H_n (Section 3.3). Described as a classical default value; no sensitivity analysis.
  • latent dimension q = int(p/10)+1
    Heuristic for the number of latent dimensions in the VAE, described in Appendix A. Chosen by hand.
assumptions (5)
  • standard math VAE evidence lower bound (ELBO) formulation and reparameterization trick are valid for the proposed loss.
    Used in Section 3.1 for the loss function; standard variational autoencoder background.
  • standard math Kernel density estimation with Silverman's or Scott's rule-of-thumb bandwidth is consistent.
    Used to estimate f_hat(y) for weights (Section 3.2) and to define H_n for the smoothed bootstrap (Section 3.3).
  • standard math Smoothed bootstrap is consistent in the Mallows metric (De Martini and Rapallo 2008; Falk and Reiss 1989).
    Cited in Section 3.3 to justify the generative process.
  • domain assumption The VAE's latent space is regular enough (continuity and completeness) for kernel smoothing to generate valid samples.
    Central to DAVID; the authors argue VAE ensures this, but it is an empirical property that may fail for tabular data (they cite Shwartz-Ziv and Armon 2022).
  • domain assumption Rare target values are those with low empirical density f_hat(y), and upweighting them during VAE training improves reconstruction and generation of rares.
    The core premise of the balanced loss, assumed throughout Section 3.2.

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Pith. "Pith review of Data Augmentation with Variational Autoencoder for Imbalanced Dataset." pith.science (2026). https://pith.science/paper/MDZGAIT7

@misc{pith2026241207039,
  author       = {Pith},
  title        = {Pith review of: Data Augmentation with Variational Autoencoder for Imbalanced Dataset},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MDZGAIT7}},
  note         = {Machine review of arXiv:2412.07039}
}
read the original abstract

Learning from an imbalanced distribution presents a major challenge in predictive modeling, as it generally leads to a reduction in the performance of standard algorithms. Various approaches exist to address this issue, but many of them concern classification problems, with a limited focus on regression. In this paper, we introduce a novel method aimed at enhancing learning on tabular data in the Imbalanced Regression (IR) framework, which remains a significant problem. We propose to use variational autoencoders (VAE) which are known as a powerful tool for synthetic data generation, offering an interesting approach to modeling and capturing latent representations of complex distributions. However, VAEs can be inefficient when dealing with IR. Therefore, we develop a novel approach for generating data, combining VAE with a smoothed bootstrap, specifically designed to address the challenges of IR. We numerically investigate the scope of this method by comparing it against its competitors on simulations and datasets known for IR.

Figures

Figures reproduced from arXiv: 2412.07039 by the authors.

Figure 1
Figure 1. DAVID Algorithm: Data Generation 4 Numerical Illustration 4.1 Dataset We first test our approach on a simple simulated dataset of size 3,000. To do this, we simulate 6 numerical features X = Xj , j = 1, · · · , 6 and 1 target variable Y as follows: • Features X : X1 ∼ N (0, 2) ; X2 ∼ N (10, 2) ; X3 ∼ N (0, 5) ; X4 ∼ N (X 3 1 , 1) ; X5 ∼ N ((X2 − 10)2 , 1) ; X6 ∼ N (X 2 3 , 2) • Target variable Y : Y ∼ N (U 2 , 10) w… view at source ↗

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Forward citations

Cited by 2 Pith papers

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  2. CARTGen-IR: Synthetic Tabular Data Generation for Imbalanced Regression

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    A CART-based synthetic sampler with rarity-weighted resampling achieves state-of-the-art competitive results for imbalanced regression without target thresholds.

Reference graph

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