Technical Summary: The Hidden Cost of Resampling in Tree Ensembles

1. Problem Statement

Class imbalance is pervasive in high-stakes domains such as fraud detection and disease screening. The standard remedy involves resampling techniques—specifically Synthetic Minority Over-sampling Technique (SMOTE), random oversampling (ROS), and random undersampling (RUS)—to balance training sets. While these methods are routinely evaluated using discrimination metrics (e.g., F1-score, AUC, minority-class recall), they are almost never assessed for probability calibration.

Many deployed systems rely on predicted probabilities for downstream decisions (e.g., expected-cost optimization, triage thresholds). Resampling deliberately distorts the class prior observed during training, leading to the hypothesis that it also distorts the emitted probabilities. This paper investigates whether resampling degrades the calibration of tree ensembles, how this degradation scales with the imbalance ratio (IR), and whether post-hoc corrections can repair the damage without sacrificing ranking power.

2. Methodology

The study employs a rigorous, multi-seed, paired-statistics experimental design across five public binary classification datasets (Imbalance Ratios ranging from 1.9 to 70.1) and two tree ensemble models: Random Forests (RF) and Histogram Gradient Boosting (HGB).

• Experimental Conditions:
  • Baseline: No resampling.
  • Resampling: SMOTE, ROS, and RUS (targeting 1:1 class balance within training folds).
  • Control: Class-weighting (rebalancing loss without data modification).
  • Post-hoc Calibration: Platt scaling and Isotonic regression applied to SMOTE models on a held-out calibration split.
• Metrics:
  • Calibration: Expected Calibration Error (ECE), Brier score, and reliability diagrams.
  • Discrimination: ROC-AUC, PR-AUC, and minority-class F1.
• Statistical Analysis: Comparisons utilize the paired Wilcoxon signed-rank test across 10 random seeds and 5-fold cross-validation. Effect sizes are quantified using Cliff's $\delta$. Holm–Bonferroni correction is applied to control family-wise error rates.
• Specific Investigations:
  • H1: Does resampling degrade calibration?
  • H2: Can post-hoc recalibration repair the damage?
  • H3: How does the damage scale with imbalance ratio and oversampling aggressiveness?
  • H4 (Negative Result): Does the analytic prior-shift correction (valid for undersampling) transfer to SMOTE?

3. Key Results

A. Resampling Degrades Calibration (H1)

All resampling families significantly increase ECE compared to the baseline, though the magnitude varies drastically:

• SMOTE & ROS: Cause a small-to-moderate increase in ECE (e.g., SMOTE: $0.052 \to 0.061$, $\delta = +0.27$).
• Random Undersampling (RUS): Causes severe degradation, particularly at high imbalance ratios. On the yeast_ml8 dataset (IR=70), RUS inflates ECE from $0.008$ to $0.395$. This is attributed to "sample-size collapse" (training on $\sim50$ samples) rather than the resampling mechanism itself, though RUS remains damaging on datasets with adequate sample sizes.
• Class Weighting: Causes only marginal calibration shifts, indicating the harm stems from altering the training data distribution, not merely the objective function.

B. Post-hoc Recalibration Repairs Damage (H2)

A single post-hoc recalibration step (Platt or Isotonic) effectively eliminates the calibration damage caused by SMOTE:

• ECE Reduction: SMOTE's ECE drops from $0.061$ to $0.021$ (Platt) and $0.025$ (Isotonic), often falling below the original baseline.
• Ranking Cost: The repair incurs a negligible cost to ranking power. AUC decreases by only $0.002$($\delta = -0.07$). This minor drop is largely attributed to the data reduction required for the calibration split, not the transformation itself.
• Trade-off: Trading a $0.002$ AUC drop for a $66\%$ reduction in ECE is favorable for decision-making systems.

C. Scaling with Imbalance and Aggressiveness (H3)

• Imbalance Ratio: The calibration damage from RUS grows steeply with the imbalance ratio. In contrast, SMOTE's calibration penalty remains relatively small and stable across the studied IR range (1.9–70).
• Oversampling Ratio: Calibration error grows monotonically with the aggressiveness of SMOTE (the amount of synthetic data injected), while discrimination metrics (AUC, F1) remain flat or slightly improve.

D. Analytic Correction Fails for SMOTE (Negative Result)

The paper demonstrates that the analytic prior-shift correction (which works for RUS by adjusting for the shifted prior $\pi_{train}$) does not transfer to SMOTE.

• Reasoning: RUS shifts only the prior $p(y)$, leaving the class-conditional density $p(x|y)$ intact. SMOTE, however, synthesizes new points via interpolation, thereby distorting the class-conditional density $p(x|y=1)$.
• Outcome: Applying the analytic correction to SMOTE models fails to improve ECE (even worsening it in some cases), whereas data-driven isotonic recalibration succeeds.

E. Feature Attribution Stability

SHAP analysis on the credit-g dataset indicates that SMOTE preserves the learned feature structure (Spearman correlation of 0.96 in feature importance rankings) while corrupting the probability scale. This confirms that the calibration damage is a scaling issue correctable by monotone transforms, not a fundamental change in what the model learns.

4. Significance and Contributions

The authors position this work not as a discovery of a novel phenomenon (as the calibration damage of undersampling was previously noted by Dal Pozzolo et al.), but as a practical, evidence-based consolidation and extension of existing knowledge.

• Clarification of Risk: The study distinguishes between "small but real" calibration costs for SMOTE and "genuinely dangerous" costs for RUS, especially at extreme imbalance ratios.
• Practical Guide: It provides a clear protocol for practitioners: if resampling is used and probabilities drive decisions, a post-hoc recalibration step is necessary and sufficient.
• Methodological Correction: It explicitly warns against applying analytic prior-shift corrections to synthetic oversampling methods, as they fail to account for density distortion.
• Evaluation Standard: The paper argues that imbalanced learning studies must report calibration metrics (ECE, Brier) alongside discrimination metrics (F1, AUC) to avoid shipping models with untrustworthy probabilities.

5. Limitations

The authors acknowledge several boundaries to their claims:

• The study is limited to tabular data and two tree ensemble models; neural networks and other modalities may behave differently.
• The decomposition of AUC loss into "data reduction" vs. "calibration transform" costs is based on a specific split ratio.
• The explanation for SMOTE's failure of analytic correction is an intuitive hypothesis regarding $p(x|y)$ distortion, requiring formal analysis in future work.
• The results are bounded by the tested imbalance range (IR 1.9–70); extreme ratios (hundreds or thousands) may yield larger effects.