Illustrated Guide to ROC and AUC

Think of a regression model mapping a number of features onto a real number (potentially a probability). The resulting real number can then be mapped on one of two classes, depending on whether this predicted number is greater or lower than some choosable threshold. Let's take for example a logistic regression and data on the survivorship of the Titanic accident to introduce the relevant concepts which will lead naturally to the ROC (Receiver Operating Characteristic) and its AUC or AUROC (Area Under ROC Curve). Every record in the data set represents a passenger – providing information on her/his age, gender, class, number of siblings/spouses aboard (sibsp), number of parents/children aboard (parch) and, of course, whether s/he survived the accident. The logistic regression model is tested on batches of 10 cases with a model trained on the remaining N-10 cases – the test batches form a partition of the data. In short, Leave-10-out CV has been applied to arrive at more accurate estimation of the out-of-sample error rates.