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REVIEW 3 major objections 6 minor 41 references

Imbalance-XGBoost: Leveraging Weighted and Focal Losses for Binary Label-Imbalanced Classification with XGBoost

T0 review · 3 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Imbalance-XGBoost lets XGBoost learn binary classification with skewed labels by plugging in weighted cross-entropy and focal losses, and reports F1 up to 0.89 on a Parkinson's dataset.

desk verdict The package is real and the focal-loss algebra is right, but the weighted-loss gradients are wrong and the empirical F1 gains sit close to a trivial all-positive baseline. read the letter →

arxiv 1908.01672 v2 pith:KJRBPXSN submitted 2019-08-05 cs.LG stat.ML

Chen Wang , Chengyuan Deng , Suzhen Wang This is my paper · ORCID
classification cs.LGstat.ML
keywords imbalancedclassificationXGBoostPythonpackageweightedcross-entropyfocallossgradientboostingbinaryParkinson'sdisease
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 claims that XGBoost can be turned into a general-purpose learner for binary label-imbalanced classification by swapping its default objective for either a weighted cross-entropy loss or a focal loss. Its contribution is a small Python package, Imbalance-XGBoost, that implements both losses through XGBoost's custom-objective mechanism, together with an algebraic derivation of the first- and second-order derivatives the training loop requires. On a Parkinson's disease dataset with a patient-to-healthy ratio of roughly 3:1, the package reports F1 scores of 0.85–0.89 across feature groups, exceeding the comparison figures from the original dataset study, while accuracy falls slightly in each case. The result matters because XGBoost is one of the most widely used tools for skewed, large-scale classification tasks, and the package plugs the loss functions directly into that workflow.

What carries the argument

The machinery is XGBoost's second-order approximation of the boosting objective, in which each split is scored from per-example first derivatives $g_i$ and second derivatives $h_i$ of the loss with respect to the raw prediction. Since XGBoost does not differentiate losses itself, Imbalance-XGBoost supplies these two numbers for each loss through custom objective classes: for weighted cross-entropy the paper derives merged-form expressions using $\hat{y}_i=\sigma(z_i)$ and the sigmoid identity $\partial \hat{y}_i/\partial z_i=\hat{y}_i(1-\hat{y}_i)$; for focal loss it derives a lengthier expression (Eqs. 10 and 11) with shorthand variables $\eta_1,\dots,\eta_5$ to keep the implementation vectorizable. These derivatives are what let the two losses run inside XGBoost without changing the boosting engine.

What would settle it

Train the package's weighted objective on a small synthetic binary dataset with both classes present, then numerically compute the derivative of the loss in equation (4) at the fitted model; if that derivative is not near zero even though the boosting run has converged, the supplied gradient and Hessian do not match the loss the paper claims to minimize.

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Extended reading notes

Core claim

The central discovery the paper argues for is that two imbalanced-aware loss functions, weighted cross-entropy and focal loss, can be implemented inside XGBoost purely through the software's custom objective framework by supplying hand-derived gradient and Hessian expressions. Weighted cross-entropy multiplies the loss on the positive class by a parameter α, while focal loss adds a $(1-\hat{y})^{\gamma}$ down-weighting factor so the classifier concentrates on hard examples. On the Parkinson's disease data, both variants raise F1 over the best previously reported results on the same feature sets while lowering accuracy, and the focal variant is the stronger of the two, reaching F1 0.89 on the top-50 features selected by a minimum-redundancy maximum-relevance criterion, versus 0.84 for the best model in the original study. The paper also claims that this is the first integrated implementation of the two losses in XGBoost, making the derivative derivation a substantive part of the contribution.

Load-bearing premise

The load-bearing premise is that equations (5) and (6) are the true gradient and Hessian of the weighted cross-entropy loss for every training example, including the negative class; when this algebraic identity fails, the weighted model is not minimizing the loss the paper says it minimizes.

Editorial extensions

If this is right

  • A user can select the imbalanced objective at construction time with a keyword such as `special_objective='weighted'` or `'focal'`, then tune the corresponding parameter through grid search and cross-validation in the usual estimator workflow.
  • Models fit with the custom losses can be saved as plain XGBoost boosters, so a model trained with the package can be deployed later on machines that do not have the package installed.
  • On the Parkinson's dataset, the paper reports focal-XGBoost reaching F1 0.89 on the top-50 features, exceeding the 0.84 best previous comparison, with accuracy 0.83 instead of 0.86.
  • Because the losses are handled at the objective level, they can be combined with existing data-level resampling steps in an estimator pipeline, giving users both algorithm-level and data-level imbalance remedies.
  • The same hand-derived derivatives can be reused outside the package in any XGBoost-style workflow that accepts custom objectives, including one-vs-all multi-class setups.

Reading between the lines

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

  • The merged-form derivative expressions are written without reference to a specific number of classes, so they can be carried over to one-vs-all multi-class ensembles or to other boosting libraries that accept custom objectives; that porting is mechanical once the package's formulas are transcribed.
  • If the weighted-loss gradient is corrected for negative examples, the accuracy-versus-F1 trade-off the paper reports for weighted-XGBoost may shift; a synthetic benchmark with a known optimal decision boundary would separate that correction from the focal-loss behavior.
  • The consistent pattern of lower accuracy with higher F1 across every feature group points to majority-class overprediction as the dominant failure mode of the prior classifiers, suggesting that F1 or a related metric should be the default reporting choice on skewed medical data.
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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

3 major / 6 minor

Summary. The paper presents Imbalance-XGBoost, an open-source Python package that implements weighted cross-entropy and focal losses as custom objectives for XGBoost in binary label-imbalanced classification. The authors describe the package design, provide first- and second-order derivative derivations for the two losses, and empirically evaluate the implementation on a Parkinson's disease classification dataset, reporting higher F1 scores than the baseline study and claiming multiple state-of-the-art performances.

Significance. The intended contribution is practically useful if it holds: an XGBoost-compatible implementation of weighted and focal losses would give practitioners two standard imbalance-robust objectives without leaving the XGBoost framework. The focal-loss derivative derivation appears algebraically self-contained and correct, and the package's scikit-learn integration plus public release on GitHub and PyPI are concrete engineering contributions. However, the weighted-loss part of the derivation is wrong for the negative class, and the evaluation protocol leaks information from the test data into model selection. As a result, the central claims about the weighted-loss implementation and the reported state-of-the-art performances are not currently supported.

major comments (3)
  1. [§3.2, Eqs. (5)-(6)] The stated gradient and Hessian of the weighted cross-entropy loss are incorrect for y_i = 0. For y_i = 0, Eq. (4) reduces to L = -log(1 - ŷ_i), whose derivative with respect to the raw prediction z_i is ŷ_i, and whose second derivative is ŷ_i(1 - ŷ_i). Eq. (5) gives 0 and Eq. (6) gives 0. Because XGBoost's custom-objective interface consumes only the supplied g_i and h_i, all negative-class instances contribute nothing to the tree-fitting objective. The implemented 'weighted cross-entropy' therefore does not minimize the loss in Eq. (4); it is at best a positive-only loss. This is a load-bearing error for the paper's algebraic-derivation contribution and for the package's claim to implement weighted cross-entropy.
  2. [Listing 2 and §5.1-5.2] The experimental protocol leaks information from the evaluation data into model selection. In Listing 2, GridsearchCV is applied to the full dataset to select α and γ, and the same full dataset is then used for the leave-one-object-out evaluation in §5.1-5.2. Instantiating a new booster with the selected parameters does not remove this leakage because the parameter choice itself was informed by the full dataset. A nested cross-validation or a separate validation set is required before the reported F1 values can be interpreted as honest estimates, and the 'state-of-the-art performances' claim is not supported without such a protocol.
  3. [§5.2, Tables 2-3] Several reported F1 values (for example 0.85 in Table 2 and 0.88-0.89 in Table 3) are close to the F1 of a trivial all-positive classifier on this dataset: with 188 patients and 64 healthy controls, per-record all-positive classification gives F1 = 2·188/(2·188 + 64) ≈ 0.854. The paper provides no vanilla-XGBoost baseline or class-weighted baseline, and no statistical comparison. Given that Eqs. (5)-(6) drop all negative examples, the empirical section cannot distinguish a genuine improvement from the effect of ignoring the negative class. The abstract's 'multiple state-of-the-art performances' claim is therefore not established.
minor comments (6)
  1. [§3.2, Eq. (6)] The notation ∂L²_w/∂²z_i is nonstandard; it should be written as ∂²L_w/∂z_i².
  2. [§3.2, Eq. (4)] Eq. (4) has an unmatched closing parenthesis and should be rewritten for clarity.
  3. [Listing 2 and §2.2] Variable names are inconsistent and misspelled (for example 'xgboster_focal' versus 'xgboost_focal_opt', and 'cross-validatoin'); these should be corrected.
  4. [§5.1] There are typos such as 'Parkison's disease' and 'confusion metric' where 'confusion matrix' is intended.
  5. [§3.2] The explanation after Eq. (5) reads 'a αyi term is added to control the present of the parameter'; this should be clarified, since 'presence' is presumably intended.
  6. [§6] The conclusion states that the package 'successfully combines' both losses, but this claim is not supported for the weighted loss until Eqs. (5)-(6) are corrected and the experiments are re-run.

Circularity Check

1 steps flagged · score 2.0 of 10

Minor empirical circularity: hyperparameters are tuned on the same Parkinson's dataset whose leave-one-out scores are then reported as state-of-the-art; the derivative derivations are otherwise self-contained.

  1. fitted input called prediction [Section 5.1 (Dataset and Setup), Listing 2; abstract 'multiple state-of-the-art performances']
    "Therefore, in our experiments, grid search is applied through the GridsearchCV() of Scikit-learn to explore the optimal models. The searching range of α is set to [0.2, 0.4, 0.6, 0.8, 1.0] and parameter γ is selected from the candidacies of [1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0]."

    The grid search selects α and γ by fitting on the same Parkinson's dataset (X, y) via Scikit-learn's GridsearchCV, and Listing 2 then instantiates the booster with those best parameters and reports cross_validate(..., X=x, y=y) on the same data. The reported F1 scores in Tables 2-3 are therefore fitted values reflecting hyperparameters chosen on the evaluation set, not independent predictions. The abstract's 'multiple state-of-the-art performances' claim thus reduces to a model-selection result on the test data rather than an out-of-sample prediction. This is partial empirical circularity; it does not affect the algebraic derivative derivations.

full rationale

The mathematical core is self-contained: Section 3.2 and 3.3 state the loss functions in Eqs. (4) and (7), invoke the sigmoid identity Eq. (3), and produce Eqs. (5)-(6) and (8)-(11) by direct differentiation. These derivations do not depend on the fitted α or γ, and no load-bearing self-citation is used; references to [1] and [12] supply external definitions. The single circular element is empirical: α and γ are chosen by GridsearchCV on the same Parkinson's dataset that is later used for the leave-one-out evaluation (Section 5.1, Listing 2), so the 'state-of-the-art' F1 values are fitted to the test distribution rather than independently predicted. I do not score the apparent algebraic defect in Eq. (5) for y_i=0 as circularity; it is a correctness issue, not a reduction of the claimed result to its own input. Therefore the circularity score is low (2).

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

The central derivation needs the Taylor approximation from XGBoost, the sigmoid identity, the loss definitions, and the tooling assumption that custom objectives require hand-derived derivatives. The empirical claim additionally assumes the grid-searched LOO setup is unbiased and that the [39] results form a fair baseline. The only fitted numeric parameters are alpha and gamma; XGBoost hyperparameters are not reported.

free parameters (2)
  • alpha = Grid-searched over [0.2, 0.4, 0.6, 0.8, 1.0]; best values not reported per feature set
    Weight parameter for weighted cross-entropy loss; selected on the full dataset via GridSearchCV before the final LOO evaluation.
  • gamma = Grid-searched over [1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0]; best values not reported
    Focusing parameter for focal loss; selected on the full data. The reported F1 gains are conditioned on these fitted values.
assumptions (6)
  • standard math The second-order Taylor approximation of the additive boosting objective (Eq. 2) is the correct foundation for XGBoost's custom objective framework.
    Taken from Chen and Guestrin [1]; not re-derived, but standard.
  • standard math Sigmoid activation satisfies sigma'(z)=sigma(z)(1-sigma(z)) for binary outputs.
    Eq. (3), a standard property used throughout the derivative derivations.
  • domain assumption The loss definitions in Eqs. (4) and (7) match the intended weighted and focal losses.
    Weighted loss is the conventional cost-sensitive cross entropy; focal loss is from [12]. If the intended losses differ, the derivatives apply to the wrong target.
  • domain assumption Leave-one-object-out cross-validation after grid search on the full dataset gives an unbiased estimate of generalization.
    The grid search in Section 5.1 uses GridSearchCV on all data, and the same data is then used for the reported LOO results; this assumption is questionable and load-bearing for the SOTA claim.
  • domain assumption The baseline numbers from [39] are a fair and current state-of-the-art comparison.
    Only baseline considered; no vanilla XGBoost, scale_pos_weight, or other imbalanced-learning methods are compared.
  • domain assumption XGBoost custom objectives require user-provided gradient and Hessian; no automatic differentiation is available.
    Tooling assumption stated in Section 3.1; motivates the derivative derivations.

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Cite this review

Pith. "Pith review of Imbalance-XGBoost: Leveraging Weighted and Focal Losses for Binary Label-Imbalanced Classification with XGBoost." pith.science (2026). https://pith.science/paper/KJRBPXSN

@misc{pith2026190801672,
  author       = {Pith},
  title        = {Pith review of: Imbalance-XGBoost: Leveraging Weighted and Focal Losses for Binary Label-Imbalanced Classification with XGBoost},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KJRBPXSN}},
  note         = {Machine review of arXiv:1908.01672}
}
read the original abstract

The paper presents Imbalance-XGBoost, a Python package that combines the powerful XGBoost software with weighted and focal losses to tackle binary label-imbalanced classification tasks. Though a small-scale program in terms of size, the package is, to the best of the authors' knowledge, the first of its kind which provides an integrated implementation for the two losses on XGBoost and brings a general-purpose extension on XGBoost for label-imbalanced scenarios. In this paper, the design and usage of the package are described with exemplar code listings, and its convenience to be integrated into Python-driven Machine Learning projects is illustrated. Furthermore, as the first- and second-order derivatives of the loss functions are essential for the implementations, the algebraic derivation is discussed and it can be deemed as a separate algorithmic contribution. The performances of the algorithms implemented in the package are empirically evaluated on Parkinson's disease classification data set, and multiple state-of-the-art performances have been observed. Given the scalable nature of XGBoost, the package has great potentials to be applied to real-life binary classification tasks, which are usually of large-scale and label-imbalanced.

Figures

Figures reproduced from arXiv: 1908.01672 by the authors.

Figure 1
Figure 1. The Overall Structure of the Program The overall program is consist of three classes: one main class imbalance_xgboost, which contains the method the users will be applying, and two customized-loss classes, Weight_Binary_Cross_Entropy and Focal_Binary_Loss, on which the imbalanced losses are based. The loss functions are designed as separate classes for the convenience of parameter tuning, and they are not supposed … view at source ↗

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