# AUC (Average Precision)

May 20, 2023

In the field of Artificial Intelligence and Machine Learning, the term AUC (Area Under the Curve) often refers to the evaluation of binary classification models. In this context, AUC is a measure of the overall ability of the model to distinguish between positive and negative classes. The AUC metric estimates the probability that a randomly selected positive instance is ranked higher than a randomly selected negative instance.

## Mathematical Definition of AUC

The AUC metric is defined as the area under the Receiver Operating Characteristic (ROC) curve. The ROC curve is a plot of the True Positive Rate (TPR) against the False Positive Rate (FPR) for different classification thresholds. The TPR is the proportion of actual positive instances that are correctly classified as positive, while the FPR is the proportion of actual negative instances that are incorrectly classified as positive.

The ROC curve is obtained by varying the classification threshold and computing the TPR and FPR for each threshold. The AUC is then calculated by integrating the ROC curve between FPR = 0 and FPR = 1.

In other words, AUC represents the probability that a randomly selected positive instance will be ranked higher than a randomly selected negative instance, according to the model’s predictions.

## Calculation of AUC

To calculate AUC, we first need to obtain the ROC curve for a given binary classification model. This can be done by varying the classification threshold and computing the TPR and FPR for each threshold.

```
# Example code in Python to calculate AUC
from sklearn.metrics import roc_auc_score
y_true = [0, 0, 1, 1] # actual class labels
y_scores = [0.1, 0.4, 0.35, 0.8] # predicted scores
auc = roc_auc_score(y_true, y_scores)
print("AUC: ", auc)
```

In the above code, we use the `roc_auc_score`

function from the scikit-learn library to calculate AUC for a binary classification problem with four instances. `y_true`

represents the actual class labels (0 for negative and 1 for positive), while `y_scores`

represents the predicted scores. The `roc_auc_score`

function returns the AUC value.

## Interpretation of AUC

The interpretation of AUC depends on the context of the problem. Generally, a higher AUC value indicates better discrimination between positive and negative classes. An AUC of 1.0 indicates perfect classification, while an AUC of 0.5 indicates random guessing.

For example, in a medical diagnosis problem where the positive class represents patients with a disease, a higher AUC means that the model is better at correctly identifying patients with the disease and ruling out patients without the disease.

## Applications of AUC

AUC is a widely used metric in the evaluation of binary classification models. It has several applications in different fields, such as:

**Medical diagnosis:**AUC can be used to evaluate the performance of diagnostic models that predict the presence or absence of a disease based on patient data.**Marketing:**AUC can be used to evaluate the effectiveness of marketing campaigns that aim to target specific customer segments based on their behavior or characteristics.**Fraud detection:**AUC can be used to evaluate the performance of fraud detection models that identify fraudulent transactions based on historical data.

## AUC vs. Accuracy

AUC is often used as an alternative to accuracy in the evaluation of binary classification models. While accuracy measures the proportion of correctly classified instances, AUC measures the ability of the model to distinguish between positive and negative classes, taking into account the trade-off between TPR and FPR.

In some cases, accuracy may not be an appropriate metric for evaluating classification models, especially when the classes are imbalanced or the misclassification costs are asymmetric. In these cases, AUC can provide a more informative evaluation of the model’s performance.