Inadequate Holdout Set Sizing for Rare Events in Machine Learning

Introduction

Rare event prediction is a critical domain in machine learning (ML) – often encountered in fields like healthcare, finance, cybersecurity, and engineering, where the events of greatest interest (e.g., fraud, disease outbreak, system failure) occur infrequently, sometimes at rates well below 1%. When building models for such targets, a fundamental challenge is evaluating those models fairly and reliably—especially when using a holdout (test) set. An inadequate holdout set—most often too small—can drastically undermine your ability to detect, estimate, and generalize performance for rare events.

Why Holdout Set Size Matters for Rare Events

• Skewed Class Distribution: In rare event scenarios, the vast majority of data belongs to the “majority” (nonevent) class, while the minority (“event”) class may have only a handful of samples, even in large datasets.
• Biases and Large Uncertainty: A small holdout set is unlikely to contain enough, or sometimes any, rare event examples—making statistical estimations (precision, recall, ROC AUC, etc.) highly unstable, with wide confidence intervals. This may lead to gross over- or underestimation of model utility.
• Overfitting and Poor Generalization: If you reserve too little data for validation, your model may look artificially strong due to “chance hits” or the peculiarities of a few data points, rather than true predictive skill on unseen real-world cases.

Statistical Impact of Inadequate Holdout Sizing

• Large Confidence Intervals: The fewer rare event cases in your holdout, the wider your uncertainty. For example, seeing 0, 1, or 2 rare events out of 100 holdout observations makes calculated rates statistically noisy and unreliable.
• Risk of No Rare Events At All: Especially in very rare events, a holdout set might contain zero examples of the minority class, making any class-specific validation impossible—your reported recall or F1 score could be undefined.
• Non-Representativeness: A small or poorly sampled holdout set doesn’t reflect the true statistical landscape, leading to “validation leakage” or failures in model deployment when exposed to new data.

Theoretical and Practical Guidance on Holdout Size

Recent work (Haidar-Wehbe et al., 2024; Liley et al., 2021) has developed theoretical frameworks for optimal holdout size selection (OHS), balancing two factors:

• Too Small: Insufficient signal to reliably estimate model performance on rare events—risks inaccurate or unstable models.
• Too Large: Wastes valuable data, withholding information that could have improved the model’s learning of rare patterns.

Key insights:

• For a dataset of size NN, the optimal holdout set size for updating risk models (under certain assumptions) scales approximately as NN, balancing statistical accuracy with opportunity cost.
• For extremely rare events, the absolute number of rare cases should be considered—a rule of thumb is to ensure at least 10–30 rare event cases fall in the validation set for reliable performance estimations, though more is usually better.
• When even after reasonable holdout splitting, rare events are too few, alternative validation strategies like repeated cross-validation, bootstrapping, or aggregating results over multiple runs are preferred to one-off holdout testing.

Consequences of Inadequate Holdout Sizing: A Case Example

In studies of clinical risk scores (e.g., pre-eclampsia), if the holdout set is small, the updated model becomes inaccurate—negatively impacting future patient care. Theoretical results and empirical demonstrations show that an inadequately sized holdout set leads to suboptimal, sometimes harmful, risk estimation for the minority class, while an appropriately chosen holdout set reduces the cost (in terms of adverse events) asymptotically optimally—often matching the best possible (oracle) strategy in practice.

Recommendations

• Estimate the Number of Rare Events in Holdout Beforehand: Target at least 10–30 event cases, more for high-stakes or multi-class tasks.
• Don’t Rely on Single Holdout Splits for Small Datasets: Use cross-validation or bootstrap approaches, especially when the total number of rare events is low.
• Formally Assess the Learning Curve: Study how your model’s error declines with more data, and adjust holdout size to minimize overall risk while ensuring enough signal for model updating.
• Trade-Off Management: Remember, increasing holdout size reduces the benefit for those in the holdout group (e.g., missing out on interventions) but increases the reliability of future interventions for everyone else—a critical ethical and statistical consideration, especially in healthcare.

Conclusion

Size matters—a lot—for holdout sets in rare event prediction. An inadequately sized holdout, especially one with too few (or no) rare events, results in volatile, unreliable model evaluation, which can cascade into poor real-world decision-making. With careful sizing—grounded in empirical, theoretical, and cost-benefit trade-offs—you can ensure rare event models genuinely deliver the value promised in high-risk, high-impact applications.