{"id":2237,"date":"2025-08-07T16:06:37","date_gmt":"2025-08-07T16:06:37","guid":{"rendered":"https:\/\/www.mhtechin.com\/support\/?p=2237"},"modified":"2025-08-07T16:06:37","modified_gmt":"2025-08-07T16:06:37","slug":"inadequate-holdout-set-sizing-for-rare-events-in-machine-learning","status":"publish","type":"post","link":"https:\/\/www.mhtechin.com\/support\/inadequate-holdout-set-sizing-for-rare-events-in-machine-learning\/","title":{"rendered":"Inadequate Holdout Set Sizing for\u00a0Rare Events in\u00a0Machine Learning"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">Introduction<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Rare event prediction<\/strong>&nbsp;is a critical domain in machine learning (ML) \u2013 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\u2014especially when using a holdout (test) set. An inadequate holdout set\u2014most often too small\u2014can drastically undermine your ability to detect, estimate, and generalize performance for rare events.<a rel=\"noreferrer noopener\" target=\"_blank\" href=\"https:\/\/arxiv.org\/html\/2309.11356v2\"><\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Why Holdout Set Size Matters for Rare Events<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Skewed Class Distribution<\/strong>: In rare event scenarios, the vast majority of data belongs to the &#8220;majority&#8221; (nonevent) class, while the minority (&#8220;event&#8221;) class may have only a handful of samples, even in large datasets.<a href=\"https:\/\/arxiv.org\/html\/2309.11356v2\" target=\"_blank\" rel=\"noreferrer noopener\"><\/a><\/li>\n\n\n\n<li><strong>Biases and Large Uncertainty<\/strong>: A small holdout set is unlikely to contain enough, or sometimes any, rare event examples\u2014making statistical estimations (precision, recall, ROC AUC, etc.) highly unstable, with wide confidence intervals. This may lead to gross over- or underestimation of model utility.<a href=\"https:\/\/pmc.ncbi.nlm.nih.gov\/articles\/PMC9464671\/\" target=\"_blank\" rel=\"noreferrer noopener\"><\/a><\/li>\n\n\n\n<li><strong>Overfitting and Poor Generalization<\/strong>: If you reserve too little data for validation, your model may look artificially strong due to &#8220;chance hits&#8221; or the peculiarities of a few data points, rather than true predictive skill on unseen real-world cases.<a href=\"https:\/\/pmc.ncbi.nlm.nih.gov\/articles\/PMC11005022\/\" target=\"_blank\" rel=\"noreferrer noopener\"><\/a><\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Statistical Impact of Inadequate Holdout Sizing<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Large Confidence Intervals<\/strong>: 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.<a href=\"https:\/\/pmc.ncbi.nlm.nih.gov\/articles\/PMC9464671\/\" target=\"_blank\" rel=\"noreferrer noopener\"><\/a><\/li>\n\n\n\n<li><strong>Risk of No Rare Events At All<\/strong>: Especially in very rare events, a holdout set might contain zero examples of the minority class, making any class-specific validation impossible\u2014your reported recall or F1 score could be undefined.<\/li>\n\n\n\n<li><strong>Non-Representativeness<\/strong>: A small or poorly sampled holdout set doesn&#8217;t reflect the true statistical landscape, leading to &#8220;validation leakage&#8221; or failures in model deployment when exposed to new data.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Theoretical and Practical Guidance on Holdout Size<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Recent work<\/strong>&nbsp;(Haidar-Wehbe et al., 2024; Liley et al., 2021) has developed theoretical frameworks for&nbsp;<strong>optimal holdout size selection<\/strong>&nbsp;(OHS), balancing two factors:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Too Small:<\/strong>\u00a0Insufficient signal to reliably estimate model performance on rare events\u2014risks inaccurate or unstable models.<\/li>\n\n\n\n<li><strong>Too Large:<\/strong>\u00a0Wastes valuable data, withholding information that could have improved the model&#8217;s learning of rare patterns.<a href=\"https:\/\/arxiv.org\/pdf\/2202.06374.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><\/a><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Key insights:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>For a dataset of size\u00a0N<em>N<\/em>, the optimal holdout set size for updating risk models (under certain assumptions) scales approximately as\u00a0N<em>N<\/em>, balancing statistical accuracy with opportunity cost.<\/li>\n\n\n\n<li>For extremely rare events, the absolute number of rare cases should be considered\u2014a rule of thumb is to ensure at least 10\u201330 rare event cases fall in the validation set for reliable performance estimations, though more is usually better.<a href=\"https:\/\/bmcmedresmethodol.biomedcentral.com\/articles\/10.1186\/s12874-023-02060-x\" target=\"_blank\" rel=\"noreferrer noopener\"><\/a><\/li>\n\n\n\n<li>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.<a href=\"https:\/\/pmc.ncbi.nlm.nih.gov\/articles\/PMC11005022\/\" target=\"_blank\" rel=\"noreferrer noopener\"><\/a><\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Consequences of Inadequate Holdout Sizing: A Case Example<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">In studies of clinical risk scores (e.g., pre-eclampsia), if the holdout set is small, the updated model becomes inaccurate\u2014negatively impacting future patient care. Theoretical results and empirical demonstrations show that an&nbsp;<strong>inadequately sized holdout set leads to suboptimal, sometimes harmful, risk estimation for the minority class<\/strong>, while an appropriately chosen holdout set reduces the cost (in terms of adverse events) asymptotically optimally\u2014often matching the best possible (oracle) strategy in practice.<a rel=\"noreferrer noopener\" target=\"_blank\" href=\"http:\/\/arxiv.org\/pdf\/2202.06374.pdf\"><\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Recommendations<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Estimate the Number of Rare Events in Holdout Beforehand<\/strong>: Target at least 10\u201330 event cases, more for high-stakes or multi-class tasks.<\/li>\n\n\n\n<li><strong>Don&#8217;t Rely on Single Holdout Splits for Small Datasets<\/strong>: Use cross-validation or bootstrap approaches, especially when the total number of rare events is low.<a href=\"https:\/\/pmc.ncbi.nlm.nih.gov\/articles\/PMC9464671\/\" target=\"_blank\" rel=\"noreferrer noopener\"><\/a><\/li>\n\n\n\n<li><strong>Formally Assess the Learning Curve<\/strong>: Study how your model&#8217;s error declines with more data, and adjust holdout size to minimize overall risk while ensuring enough signal for model updating.<a href=\"https:\/\/cran.r-project.org\/web\/packages\/OptHoldoutSize\/vignettes\/simulated_example.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><\/a><\/li>\n\n\n\n<li><strong>Trade-Off Management<\/strong>: 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\u2014a critical ethical and statistical consideration, especially in healthcare.<a href=\"http:\/\/arxiv.org\/pdf\/2202.06374.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><\/a><\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Conclusion<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Size matters\u2014a lot\u2014for 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\u2014grounded in empirical, theoretical, and cost-benefit trade-offs\u2014you can ensure rare event models genuinely deliver the value promised in high-risk, high-impact applications.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Introduction Rare event prediction&nbsp;is a critical domain in machine learning (ML) \u2013 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 [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-2237","post","type-post","status-publish","format-standard","hentry","category-support"],"_links":{"self":[{"href":"https:\/\/www.mhtechin.com\/support\/wp-json\/wp\/v2\/posts\/2237","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mhtechin.com\/support\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.mhtechin.com\/support\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.mhtechin.com\/support\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mhtechin.com\/support\/wp-json\/wp\/v2\/comments?post=2237"}],"version-history":[{"count":1,"href":"https:\/\/www.mhtechin.com\/support\/wp-json\/wp\/v2\/posts\/2237\/revisions"}],"predecessor-version":[{"id":2238,"href":"https:\/\/www.mhtechin.com\/support\/wp-json\/wp\/v2\/posts\/2237\/revisions\/2238"}],"wp:attachment":[{"href":"https:\/\/www.mhtechin.com\/support\/wp-json\/wp\/v2\/media?parent=2237"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.mhtechin.com\/support\/wp-json\/wp\/v2\/categories?post=2237"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.mhtechin.com\/support\/wp-json\/wp\/v2\/tags?post=2237"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}