Receiver operating characteristic

As explained in Machine Learning Algorithms in Depth

A receiver operating characteristic curve plots the true positive rate against the false positive rate across classification thresholds.

A receiver operating characteristic (ROC) curve evaluates a binary classifier across thresholds by plotting the true positive rate (TPR) against the false positive rate (FPR). For a confusion matrix, TPR = TP/(TP + FN) and FPR = FP/(FP + TN). section 5.2

Interpret the curve through its threshold-dependent operating points:

• Varying the classification threshold produces different TP, FP, FN, and TN values and therefore different ROC points. section 5.2
• Perfect classification reaches TPR = 1 and FPR = 0; performance generally improves toward the upper-left corner. section 5.2
• The diagonal TPR = FPR line represents chance-level performance. section 5.2
• The area under the curve (AUC) summarizes ROC quality; higher values are better, with a maximum of 1. section 5.2

Figure 5.4 Receiver operating characteristic (ROC) plot (left) and precision-recall plot (right)

Use the ROC plot alongside the precision-recall plot to compare threshold-based views of classifier performance. section 5.2

How Machine Learning Algorithms in Depth covers it

How deep it goes

Defines TPR and FPR, explains threshold-generated points, and summarizes quality with AUC.

Examples

Uses a ROC plot, the upper-left perfect-classification point, and the diagonal chance-level line.

What it assumes

Builds from binary-classifier predictions and confusion-matrix counts rather than assuming ROC measures.

What you can do after

Evaluate binary classifiers using TPR, FPR, threshold plots, and AUC.

How it connects

Connects confusion matrices, classification thresholds, precision-recall curves, and AUC.

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Related concepts

• thresholduses · A threshold is a boundary value against which a quantity is compared to determine whether a condition is met or an action or decision is triggered.
• area under the curvemeasured by · The area under a curve is the integral of its values over a specified domain and, in classification evaluation, commonly summarizes performance across decision thresholds.
• recalluses · Recall is the fraction of relevant, positive, or target outcomes that a system successfully identifies, retrieves, or captures.
• specificityuses · Specificity is the proportion of actual negative cases correctly identified as negative, also called the true-negative rate.
• precision-recall curvealternative to · A precision-recall curve is a plot of a classifier’s precision against recall as its decision threshold varies.
• logistic regressionproduced by · Logistic regression is a statistical classification model that estimates categorical outcome probabilities by applying a logistic or softmax function to a linear combination of input features.

This explainer was generated by Manning's knowledge graph from the text of Machine Learning Algorithms in Depth. The section links point to the parts of the book it draws on.