Compare two rare-event detection models statistically
Problem Description
You are tasked with evaluating two machine learning models, Model A and Model B, designed for rare-event detection (e.g., fraud, abuse, medical adverse events). A key characteristic of this problem is that positive events are extremely rare.
You have access to limited evaluation results for each model. This includes a small number of aggregated counts such as True Positives (TP), False Positives (FP), False Negatives (FN), and True Negatives (TN), or metrics like precision and recall at a specific threshold. You can assume that you have sufficient information to derive the full confusion matrix counts, but the absolute number of positive events observed is small.
Questions
- Which metrics are most appropriate for comparing these models in a rare-event setting? Explain why metrics like accuracy or ROC-AUC alone might be insufficient.
- How would you statistically compare Model A versus Model B, explicitly accounting for uncertainty?
- Describe the relevant statistical distributions and assumptions (e.g., binomial) you would use, and outline how you would compute confidence intervals for your chosen metrics.
- Detail how you would perform a hypothesis test to determine if one model is significantly better than the other.
- Given that you only have a "few numbers" (i.e., a small sample size), what practical steps would you take to make a responsible decision about which model to choose? Your answer should consider aspects such as setting appropriate thresholds, model calibration, and the impact of cost or alert-budget constraints.
Please state any assumptions you make during your analysis, such as whether the evaluation is paired or unpaired, or if you are comparing at a fixed threshold versus across the full performance curve.
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Compare two rare-event detection models statistically
Problem Description
You are tasked with evaluating two machine learning models, Model A and Model B, designed for rare-event detection (e.g., fraud, abuse, medical adverse events). A key characteristic of this problem is that positive events are extremely rare.
You have access to limited evaluation results for each model. This includes a small number of aggregated counts such as True Positives (TP), False Positives (FP), False Negatives (FN), and True Negatives (TN), or metrics like precision and recall at a specific threshold. You can assume that you have sufficient information to derive the full confusion matrix counts, but the absolute number of positive events observed is small.
Questions
- Which metrics are most appropriate for comparing these models in a rare-event setting? Explain why metrics like accuracy or ROC-AUC alone might be insufficient.
- How would you statistically compare Model A versus Model B, explicitly accounting for uncertainty?
- Describe the relevant statistical distributions and assumptions (e.g., binomial) you would use, and outline how you would compute confidence intervals for your chosen metrics.
- Detail how you would perform a hypothesis test to determine if one model is significantly better than the other.
- Given that you only have a "few numbers" (i.e., a small sample size), what practical steps would you take to make a responsible decision about which model to choose? Your answer should consider aspects such as setting appropriate thresholds, model calibration, and the impact of cost or alert-budget constraints.
Please state any assumptions you make during your analysis, such as whether the evaluation is paired or unpaired, or if you are comparing at a fixed threshold versus across the full performance curve.