Logistic regression achieved AUC 0.984 and isolation forest achieved AUC 0.882 on the 5,000-transaction sample containing 492 confirmed fraud cases (9.84%). At the F1-optimal threshold, the logistic model catches 86.8% of fraud cases with precision 97.7% — meaning 10 legitimate transactions are flagged for every 427 fraud cases correctly identified.

The balanced training sample has a fraud rate of 9.84%, compared to just 0.17% in the full 284,807-transaction dataset. This enrichment (57x over-sampling) ensures both models see enough fraud examples to learn discriminative patterns. Results should be interpreted with the original prevalence in mind when estimating expected false-positive volume in production.

Fraudulent transactions have a median isolation forest score of 0.612 versus 0.587 for legitimate transactions. Higher scores indicate observations that are easier to isolate — i.e., they fall in sparse regions of feature space. The degree of separation between these distributions reflects how well the unsupervised model can discriminate without access to the fraud label.

Of the top 20 features by coefficient magnitude, 9 are statistically significant at p < 0.05. The largest-magnitude coefficient is v4 (+0.855), indicating it has the strongest influence on fraud log-odds. Negative coefficients reduce estimated fraud probability while positive coefficients increase it — features like V14 and V17 are well-known fraud discriminators in this dataset.

Logistic regression achieves AUC = 0.984 and isolation forest achieves AUC = 0.882 on this dataset. AUC measures the probability that a randomly chosen fraud transaction is ranked above a randomly chosen legitimate transaction. The model closer to the top-left corner at any given false-positive rate is preferable for production use where analyst capacity limits review volume.

Under the class imbalance present in the sample (9.8% fraud), precision-recall curves provide a more honest picture of operational performance than ROC curves. A model with high PR-AUC maintains strong precision even as recall is pushed toward 1.0, minimising the number of legitimate transactions sent to a human reviewer for each additional fraud case caught.

At the F1-optimal threshold of 0.428, the logistic model correctly identifies 427 of 492 fraud cases (recall = 86.8%) while generating 10 false positives. 65 fraud cases are missed (false negatives), and these represent the highest operational risk — transactions that pass through undetected.

The 20 transactions with the highest combined anomaly score include 20 confirmed fraud cases and 0 legitimate transactions flagged as highly anomalous. The blended score averages the normalised isolation forest score and the logistic regression probability, prioritising transactions that both models agree are suspicious. Transaction amount ranges from $0 to $1218.89 across the top 20.

The most important feature for isolation forest is v19 — the PCA component on which the model most frequently and shallowly splits to isolate anomalies. Features that appear at shallow splits are particularly discriminating because they alone can separate outliers from the bulk of the data. Comparing this ranking to the logistic regression coefficients reveals whether supervised and unsupervised methods agree on which PCA components carry fraud signal.