Area under the curve

As explained in Statistics Every Programmer Needs

The area under the ROC curve is a measure of a binary classifier's ability to discriminate between positive and negative classes across classification thresholds.

AUC summarizes a binary classifier’s ability to distinguish positive from negative classes across classification thresholds. Unlike accuracy, it focuses on discrimination, which can reveal weakness on an imbalanced dataset. section 5.2.4

AUC ranges from 0 to 1; values near 1 indicate strong performance. A value of 0.5 corresponds to random guessing. AUC and accuracy can differ, though they aligned for a balanced raisin-classification example. section 5.2.4

Scikit-learn evaluation

For raisin classification, roc_auc_score returned 0.8678, matching the model’s 86.78% accuracy in this balanced example. section 5.2.4

Figure 5.4 A ROC curve. The false positive rate is plotted along the x axis, and the true positive rate is plotted along the y axis. When the curve, represented by the solid line, hugs the upper-left quadrant of the plot, as it does here, it increases the area under the curve. The dashed line represents an AUC equal to 0.5, or the equivalent of random guessing.

The ROC plot relates false-positive and true-positive rates; a curve nearer the upper-left corner encloses more area. section 5.2.4

How Statistics Every Programmer Needs covers it

How deep it goes

Defines AUC, interprets its range, contrasts it with accuracy, and demonstrates a scikit-learn calculation.

Examples

Uses raisin classification and an imbalanced exam-pass example to contrast AUC with accuracy.

What it assumes

Assumes binary class labels but does not state other prerequisites.

What you can do after

Apply scikit-learn’s roc_auc_score to evaluate binary-classifier discrimination.

How it connects

Connects ROC curves and classification thresholds with accuracy, class imbalance, and logistic regression.

liveBookmanning.com

Read Statistics Every Programmer Needs on liveBook Get the book at manning.com

Also explained in

• 

  liveBookmanning.com
  Grokking Machine LearningA scalar performance metric equal to the area under a receiver operating characteristic curve.
• 

  liveBookmanning.com
  Statistics Slam DunkAUC is the area under a receiver operating characteristic curve, measuring a binary classifier's ability to rank positive cases above negative cases.
• 

  liveBookmanning.com
  Machine Learning for Tabular Data: XGBoost, Deep Learning, and AIROC AUC is the area under the receiver operating characteristic curve, measuring a binary classifier's ability to rank positive instances above negative instances.
• 

  liveBookmanning.com
  Starting Data Analytics with Generative AI and PythonA metric equal to the area under a receiver operating characteristic curve that summarizes discrimination across thresholds.
• 

  liveBookmanning.com
  Outlier Detection in PythonAUROC is the area under the receiver operating characteristic curve, measuring a scoring model's ability to rank positive cases above negative cases across classification thresholds.
• 

  liveBookmanning.com
  Machine Learning System DesignThe area under the receiver operating characteristic curve, summarizing ranking performance across classification thresholds.
• 

  liveBookmanning.com
  Grokking StatisticsThe area under the curve is the area beneath a receiver operating characteristic or precision-recall curve, summarizing performance across thresholds.
• 

  liveBookmanning.com
  Causal Inference for Data ScienceThe area under the ROC curve is a threshold-independent measure of binary classification performance based on the receiver operating characteristic curve.
• 

  liveBookmanning.com
  Graph Neural Networks in ActionThe area under a receiver operating characteristic curve, measuring a classifier's ability to rank positive examples above negative examples across thresholds.
• 

  liveBookmanning.com
  Financial AI in PracticeThe area under a receiver operating characteristic curve, summarizing a classifier’s ability to distinguish between classes across thresholds.
• 

  liveBookmanning.com
  Machine Learning Algorithms in DepthArea under the curve is a scalar summary of the area beneath a performance curve, with larger values indicating better ranking performance in the ROC sense.

Compare how 12 books explain area under the curve →

Related concepts

• classifiermeasures · A classifier is a predictive computational model that assigns inputs to one or more discrete classes or categories.
• receiver operating characteristicmeasures · A receiver operating characteristic curve plots a binary classifier’s true-positive rate against its false-positive rate as the decision threshold varies.
• cluster-based local outlier factormeasures · Cluster-based local outlier factor is an outlier detection algorithm that scores observations using cluster membership, cluster size, and distance to relevant clusters.
• precision-recall curvemeasures · A precision-recall curve is a plot of a classifier’s precision against recall as its decision threshold varies.
• outlier detectionmeasures · Outlier detection is the process of identifying observations that substantially deviate from an expected or prevailing pattern in data.

This explainer was generated by Manning's knowledge graph from the text of Statistics Every Programmer Needs. The section links point to the parts of the book it draws on.