Imbalanced & Cost-Sensitive Learning

Imbalanced Classification & Cost-Sensitive Machine Learning addresses the extreme sample skew (fraud positive prevalence $<0.01\% \sim 0.1\%$, ratios exceeding $1:10,000$) and highly asymmetric misclassification costs in financial risk modeling; it operates across 3 synergistic tiers: 1) Data Resampling (SMOTE oversampling and EasyEnsemble/BalanceCascade bagged negative downsampling); 2) Loss Re-weighting via Focal Loss $\text{FL}(p_t) = -\alpha_t (1 - p_t)^\gamma \ln(p_t)$ (dynamically suppressing gradients from easy legitimate negatives to focus capacity on hard fraud cases); 3) Cost-Sensitive Decision Matrices that explicitly quantify the asymmetric business penalties of False Positives (user friction/churn) vs False Negatives (unrecoverable financial chargebacks) to calibrate optimal threshold cutoffs.

Payment chargeback prevention, AML transaction screening, loan default risk prediction, and malicious bot mitigation.

Standard binary cross-entropy collapses into predicting all transactions as legitimate (yielding 99.99% dummy accuracy while leaking all fraud); cost-sensitive learning minimizes monetary loss while maintaining strict false-positive caps.

Derive Focal Loss $\text{FL}(p_t) = -\alpha_t (1 - p_t)^\gamma \ln(p_t)$ and explain how the focusing parameter $\gamma$ downweights easy examples?

Compare EasyEnsemble vs BalanceCascade in training multiple bagging learners over partitioned negative sample majorities?

Why is Accuracy prohibited in fraud evaluation, and how do KS statistic, PR-AUC, and Top-1% Capture Rate serve as authoritative metrics?

Derive the optimal Bayesian decision threshold $p^* = \frac{C_{\text{FP}}}{C_{\text{FP}} + C_{\text{FN}}}$ from cost matrix parameters $C_{\text{FP}}$ and $C_{\text{FN}}$?

How do unsupervised anomaly detection models (Isolation Forest, AutoEncoders) capture novel zero-day fraud without labeled positives?