# ROC Curve

## What is an ROC Curve?

The Receiver Operating Characteristic (ROC) curve is a fundamental tool used in predictive analytics and machine learning to evaluate classifier output quality. ROC curves graphically represent the performance of a binary classifier system as the discrimination threshold is varied.

The ROC curve is a plot of the True Positive Rate (TPR) against the False Positive Rate (FPR) at various threshold settings. The True Positive Rate is also known as sensitivity, recall, or probability of detection. The False Positive Rate is also known as the fall-out or probability of false alarm. The FPR is equal to 1 minus the specificity or True Negative Rate.

## ROC Curve Examples

Let's take an example where a healthcare organization wants to predict whether a patient will have a disease based on certain health parameters. Your model will predict probabilities of being diseased for each patient, and these probabilities are compared to the actual outcomes to create the ROC curve.

Below is a simple representation of how your data may look:

 has_disease age weight bp predicted_probability true 68 150 130 0.80 false 72 160 140 0.40 false 60 140 120 0.60

The "predicted_probability" column represents the model's prediction for the likelihood of the disease, based on the patient's age, weight, and blood pressure.

By varying the threshold for which we label a prediction as 'true' (e.g., if the predicted probability > 0.5, then we predict 'true'), we can calculate different TPRs and FPRs, and thus generate the ROC curve.

## Why is an ROC Curve Important?

The ROC curve is a crucial diagnostic tool in determining the best threshold for a given model and offers a more comprehensive view of how the model performs at different threshold levels. It allows us to visualize the trade-off between sensitivity (or TPR) and specificity (1 - FPR), and choose the threshold that best balances these two measures according to our specific use case.

Moreover, the area under the ROC Curve (AUC-ROC) is a single scalar value that summarizes the overall performance of the model across all thresholds, providing a useful metric for comparing different models.

## Interpreting the AUC-ROC Score

An AUC-ROC score is a measure of the overall performance of a binary classifier. A score of 0.5 signifies that the model has no discrimination capacity and is essentially making random predictions. On the other hand, a score of 1.0 signifies a perfect model. Any value between these two extremes indicates the degree of discrimination power the model possesses. Typically, the higher the AUC-ROC score, the better the model.

## ROC Curve and Multiclass Classification

Traditionally used for binary classification problems, ROC curves can be extended to situations with more than two classes. In multiclass classification scenarios, ROC curves can be drawn for each class as a one-versus-all binary classification problem, and interpreted in a similar manner.

## Limitations of ROC Curves

While ROC curves are powerful tools, they have limitations. For instance, they may not be the best choice when dealing with highly imbalanced datasets. In these cases, the majority class might dominate the minority class, leading to misleading results. Other metrics like Precision-Recall curves could provide more reliable results in such scenarios.

## ROC Curve FAQs

What is the best possible shape of an ROC curve?

• The top-left corner of the plot is the “ideal” point: a false positive rate of zero, and a true positive rate of one. So, a model with perfect discriminatory power will have an ROC curve that hugs the top left corner of the plot.

## What does AUC-ROC represent?

• AUC-ROC represents the likelihood that the classifier will rank a randomly chosen positive instance higher than a randomly chosen negative one. AUC-ROC ranges in value from 0 to 1. A model whose predictions are 100% wrong has an AUC-ROC of 0, and a model whose predictions are 100% correct has an AUC-ROC of 1.

## What is the difference between ROC Curve and Precision-Recall (PR) Curve?

• While ROC curve plots TPR vs FPR, a Precision-Recall (PR) curve plots Precision vs Recall. ROC curves should be used when there are roughly equal numbers of observations for each class, while PR curves should be used when there is a moderate to large class imbalance.

## H2O.ai and ROC Curve

H2O Driverless AI offers automated machine learning that includes automatic handling of data preprocessing, feature engineering, model selection, and hyperparameter tuning. Within its toolkit, it provides ROC curve analysis for models to assess their performance. The generated ROC curves can be leveraged to select the best model and decide the most suitable classification threshold based on business requirements. This robust, interpretable evaluation metric adds value to the predictive power of models developed in the H2O.ai platform.