The metrics part was fine, I can do confusion matrix math in my sleep.
Start by clarifying the confusion matrix for each model at threshold 0.5, then compute precision, recall, and F1 from those counts. Finally, calculate expected cost per order using the given cost parameters and compare the models to determine which minimizes cost.
Pro tip: Always tie the metric back to the business cost: a model with lower F1 might still be better if it reduces expensive false negatives. Emphasize that the optimal threshold depends on the cost ratio, not just model performance.
Note that the base rate is 0.7%, meaning 0.7% of orders are fraudulent. List the costs: flagging a transaction costs $3, friction on a legitimate flagged order costs $1, and a missed fraud costs $120.
Assume you have the number of true positives, false positives, false negatives, and true negatives for each model at threshold 0.5. If not given, state that you would need these counts to proceed.
Precision = TP / (TP + FP), Recall = TP / (TP + FN), F1 = 2 * (Precision * Recall) / (Precision + Recall). Calculate these for both models.
Expected cost = (FP * ($3 + $1)) + (FN * $120) divided by total number of orders. Alternatively, per order: (FP/N)*$4 + (FN/N)*$120. Compare the costs.
The model with lower expected cost per order is better under these costs. Discuss how changing costs or threshold would affect the decision.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This is the part I was least prepared for.
Start by formally defining the expected cost as a function of the threshold, then minimize it to derive the optimal decision rule: predict positive when the posterior probability exceeds a threshold that depends on the cost matrix. Apply the derived formula to the fraud scenario by plugging in the given costs and calibrated probabilities, and discuss practical implications.
Pro tip: Emphasize that the optimal threshold is independent of the model's calibration as long as probabilities are calibrated; if not, you must recalibrate first. Also, mention that in practice, costs may be asymmetric and unknown, so sensitivity analysis is crucial.
Let C_FP be the cost of a false positive and C_FN be the cost of a false negative. Assume correct predictions incur zero cost. The expected cost for a given instance with posterior probability p is: E[cost] = p * C_FN * I(predict negative) + (1-p) * C_FP * I(predict positive).
Minimize expected cost by predicting positive when p * C_FN > (1-p) * C_FP, which simplifies to p > C_FP / (C_FP + C_FN). Thus the optimal threshold is t* = C_FP / (C_FP + C_FN).
Assume perfect calibration, so p is the true probability of fraud. Plug in the specific costs: if a false negative (missed fraud) costs $1000 and a false positive (blocked legitimate transaction) costs $10, then t* = 10 / (10 + 1000) ≈ 0.0099. So flag as fraud if p > 0.0099.
Note that in reality, costs may vary per transaction, calibration may be imperfect, and the threshold may need to be adjusted for business constraints (e.g., limited review capacity). Also, mention that the threshold can be expressed in terms of odds: p/(1-p) > C_FP/C_FN.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Felt okay on PR-AUC vs ROC-AUC, that's a pretty standard imbalance discussion.
Start by contrasting PR-AUC and ROC-AUC in the context of class imbalance, emphasizing how PR-AUC focuses on the minority class and is more sensitive to false positives. Then explain how calibration metrics like Brier score and ECE assess the reliability of predicted probabilities, which is crucial when decisions depend on thresholds. Finally, introduce decision curve analysis as a method to evaluate clinical utility by weighing benefits and harms across different threshold probabilities.
Pro tip: Tie the discussion to Apple's product context by noting that in user-facing applications, well-calibrated probabilities and decision curves directly impact user experience and business metrics, showing you think beyond pure statistics.
Clarify that highly imbalanced classification means one class vastly outnumbers the other, and define PR-AUC and ROC-AUC, highlighting their different focuses.
Explain that ROC-AUC can be overly optimistic because it incorporates true negatives, while PR-AUC emphasizes the minority class and is more informative when the positive class is rare.
Describe Brier score as a measure of overall probability accuracy and ECE as a measure of calibration, noting that good discrimination (high AUC) does not guarantee good calibration.
Explain that DCA evaluates the net benefit of a model across different threshold probabilities, incorporating the consequences of false positives and false negatives, thus bridging statistical performance and real-world utility.
Summarize how these metrics complement each other: PR-AUC for ranking in imbalanced settings, calibration for probability reliability, and DCA for decision-making; relate to the role and company context.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Honestly the most open-ended part and probably where I gave the weakest answer.
Start by framing the problem around prevalence shift and its impact on precision, then propose an offline evaluation that uses prevalence-invariant metrics and reweighting. For online testing, describe a phased A/B test with guardrails like manual review SLAs and false accusation caps, and emphasize monitoring for drift and fairness post-launch.
Pro tip: Emphasize that offline metrics like precision are prevalence-sensitive, so use recall, AUC, and calibration instead; also highlight the importance of pre-registering guardrail thresholds to avoid p-hacking.
Use prevalence-invariant metrics (e.g., recall, AUC, calibration) and simulate prevalence shifts via importance weighting or stratified sampling. Report performance across a range of prevalences to ensure robustness.
Propose a phased rollout with a small treatment group, pre-defined guardrails (e.g., manual review SLA < 24h, false accusation rate < 0.1%), and automatic stopping rules if guardrails are breached.
Include a holdout set that is not used for training and monitor for concept drift by comparing model predictions to ground truth over time. Evaluate fairness metrics (e.g., demographic parity, equal opportunity) across user segments.
Set up dashboards to track model performance, drift detection (e.g., PSI, KL divergence), and fairness metrics. Define alert thresholds and a process for retraining or rollback.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.