Area under the ROC curve

See also: Machine learning terms

Introduction

The Receiver Operating Characteristic (ROC) curve is a widely-used visual representation of the performance of binary classifiers. It plots True Positive Rate (TPR) against False Positive Rate (FPR) over various threshold values for each classifier. The area under the ROC curve (AUC) serves as an aggregate metric that summarizes overall classifier performance across all possible threshold values.

Methodology

Calculating the AUC begins by plotting the TPR against the FPR at various threshold values. The TPR is defined as the ratio of True Positives (TPs) to all False Negatives (FNs), while the FPR is composed of False Positives (FPs) divided by all True Negatives (TNs). After selecting threshold values that allow calculation of both these rates across various classifier outputs, we can then compute both values simultaneously.

Once the ROC curve has been drawn, the Area Under Curve (AUC) can be calculated as the area beneath it. This can be done either numerical integration or by applying the trapezoidal rule: whereby the AUC is approximated as the sum of areas of multiple trapezoids under the ROC curve. While this method provides a quick and efficient approximation, numerical integration offers more accurate results.

Interpretation

The AUC (Area Under Curve) can be used to compare the performance of different classifiers. A classifier with an AUC of 1.0 is considered perfect, while one with 0.5 has no better performance than random. In reality, AUC values typically fall between 0.5 and 1.0, with higher values signifying better outcomes.

It is essential to note that the AUC does not take into account class distribution or the cost of false positives and false negatives. For instance, in situations where false negatives have a higher cost than false positives, prioritizing reducing false negatives may be more beneficial even if this leads to more false positives. In such cases, alternative metrics such as precision-recall curves or cost-sensitive ROC curves may be more suitable.

Explain Like I'm 5 (ELI5)

The ROC curve is a visual representation of how well a machine learning model can distinguish between two entities, such as sick and healthy people. The area under this curve indicates how well the model is doing - with 1 being ideal and 0.5 equaling random chance. With this information in hand, one can compare different models to determine which one does the best job at distinguishing between them.

Explain Like I'm 5 (ELI5)

Sure! Imagine you have a large basket of apples and bananas, and you need to sort them into two piles: one for apples and one for bananas. The area under the ROC curve is an indicator of your progress in sorting fruit correctly into its appropriate piles.

The ROC curve displays how often you put fruits in the correct pile, compared to how often you put them in the wrong pile. A perfect score would be 100, meaning all fruits would always be placed correctly. However, if your score were 50, that indicates you're guessing and placing fruit incorrectly just as often as not.

The area under the ROC curve is a way to measure your success at sorting fruit correctly. The larger this area, the better at sorting fruits into appropriate piles!