The Receiver Operating Characteristic (ROC) curve is a popular tool used with binary classifiers. It is very similar to the precision/recall curve. Still, instead of plotting precision versus recall, the ROC curve plots the true positive rate (another name for recall) against the false positive rate (FPR). The FPR is the ratio of negative instances that are incorrectly classified as positive. It is equal to 1 – the true negative rate (TNR), which is the ratio of negative cases that are correctly classified as negative. The TNR is also called specificity.
Plotting The ROC Curve
I will explain this by using the classification that I did in my article on Binary Classification. I will continue this from where I left in the Binary Classification. To plot the ROC curve, you first use the roc_curve() function to compute the TPR and FPR for various threshold values:
from sklearn.metrics import roc_curve fpr, tpr, thresholds = roc_curve(y_train_5, y_scores)
Then you can plot the FPR against the TPR using Matplotlib:
def plot_roc_curve(fpr, tpr, label=None): plt.plot(fpr, tpr, linewidth=2, label=label) plt.plot([0, 1], [0, 1], 'k--') # dashed diagonal plt.axis([0, 1, 0, 1]) # Not shown in the book plt.xlabel('False Positive Rate (Fall-Out)', fontsize=16) # Not shown plt.ylabel('True Positive Rate (Recall)', fontsize=16) # Not shown plt.grid(True) # Not shown plt.figure(figsize=(8, 6)) # Not shown plot_roc_curve(fpr, tpr) plt.plot([4.837e-3, 4.837e-3], [0., 0.4368], "r:") # Not shown plt.plot([0.0, 4.837e-3], [0.4368, 0.4368], "r:") # Not shown plt.plot([4.837e-3], [0.4368], "ro") # Not shown save_fig("roc_curve_plot") # Not shown plt.show()
So there is a trade-off: the higher the recall (TPR), the more false positives (FPR) the classifier produces. The dotted line represents the ROC curve of a purely random classifier; a good classifier stays as far away from that line as possible (toward the top-left corner).
In the output above, The ROC plots, the false positive rate against the true positive rate for all possible thresholds; the red circle highlights the chosen ratio (at 43.68% recall).
One way to compare classifiers is to measure the area under the curve (AUC). A perfect classifier will have a ROC AUC equal to 1, whereas a purely random classifier will have a ROC AUC equal to 0.5. Scikit-Learn provides a function to compute the ROC AUC:
from sklearn.metrics import roc_auc_score roc_auc_score(y_train_5, y_scores)
Since the ROC curve is so similar to the precision/recall (PR) curve, you may wonder how to decide which one to use. As a rule of thumb, you should prefer the PR curve whenever the positive class is rare or when you care more about the false positives than the false negatives. Otherwise, use the ROC curve.
Using The ROC Curve in Classification
Let’s now train a RandomForestClassifier and compare its ROC curve and ROC AUC score to those of the SGDClassifier. First, you need to get scores for each instance in the training set:
from sklearn.ensemble import RandomForestClassifier forest_clf = RandomForestClassifier(n_estimators=100, random_state=42) y_probas_forest = cross_val_predict(forest_clf, X_train, y_train_5, cv=3, method="predict_proba")
The roc_curve() function expects labels and scores, but instead of scores, you can give it class probabilities. Let’s use the positive class’s probability as the score:
y_scores_forest = y_probas_forest[:, 1] # score = proba of positive class fpr_forest, tpr_forest, thresholds_forest = roc_curve(y_train_5,y_scores_forest)
Now you are ready to plot the ROC. It is useful to plot the first ROC curve as well as to see how they compare:
plt.figure(figsize=(8, 6)) plt.plot(fpr, tpr, "b:", linewidth=2, label="SGD") plot_roc_curve(fpr_forest, tpr_forest, "Random Forest") plt.plot([4.837e-3, 4.837e-3], [0., 0.4368], "r:") plt.plot([0.0, 4.837e-3], [0.4368, 0.4368], "r:") plt.plot([4.837e-3], [0.4368], "ro") plt.plot([4.837e-3, 4.837e-3], [0., 0.9487], "r:") plt.plot([4.837e-3], [0.9487], "ro") plt.grid(True) plt.legend(loc="lower right", fontsize=16) save_fig("roc_curve_comparison_plot") plt.show()
As you can see in the output above, the RandomForestClassifier’s curve looks much better than the SGDClassifier’s: it comes much closer to the top-left corner. As a result, its ROC AUC score is also significantly better:
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