ROC curve and AUC in ML Python

Introduction

The ROC curve helps us see how well a model can tell apart two groups, like sick vs healthy. AUC gives a simple number to show this ability.

When checking how good a model is at distinguishing between two classes, like spam vs not spam emails.

When comparing different models to pick the best one for classification tasks.

When you want to understand the trade-off between catching positives and avoiding false alarms.

When the classes are imbalanced, and accuracy alone is misleading.

When tuning model thresholds to find the best balance for your needs.

Syntax

ML Python

from sklearn.metrics import roc_curve, auc

fpr, tpr, thresholds = roc_curve(true_labels, predicted_scores)
roc_auc = auc(fpr, tpr)

true_labels are the actual class labels (0 or 1).

predicted_scores are the model's predicted probabilities or scores for the positive class.

Examples

Calculate ROC and AUC for a small example with 4 samples.

ML Python

fpr, tpr, thresholds = roc_curve([0, 0, 1, 1], [0.1, 0.4, 0.35, 0.8])
roc_auc = auc(fpr, tpr)

Plot the ROC curve with AUC shown in the legend.

ML Python

import matplotlib.pyplot as plt
plt.plot(fpr, tpr, label=f'AUC = {roc_auc:.2f}')
plt.xlabel('False Positive Rate')
plt.ylabel('True Positive Rate')
plt.title('ROC Curve')
plt.legend()
plt.show()

Sample Model

This program trains a simple model, calculates the ROC curve and AUC, then prints the false positive rates, true positive rates, and AUC value.

ML Python

from sklearn.datasets import make_classification
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LogisticRegression
from sklearn.metrics import roc_curve, auc
import numpy as np

# Create a simple binary classification dataset
X, y = make_classification(n_samples=100, n_features=5, random_state=42)

# Split into train and test sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=42)

# Train a logistic regression model
model = LogisticRegression()
model.fit(X_train, y_train)

# Get predicted probabilities for the positive class
y_scores = model.predict_proba(X_test)[:, 1]

# Calculate ROC curve
fpr, tpr, thresholds = roc_curve(y_test, y_scores)

# Calculate AUC
roc_auc = auc(fpr, tpr)

print(f"False Positive Rates: {np.round(fpr, 2)}")
print(f"True Positive Rates: {np.round(tpr, 2)}")
print(f"AUC: {roc_auc:.3f}")

Important Notes

The ROC curve plots the true positive rate against the false positive rate at different thresholds.

AUC ranges from 0 to 1; closer to 1 means better model performance.

ROC and AUC work well even if classes are imbalanced.

Summary

ROC curve shows how well a model separates classes at different thresholds.

AUC summarizes the ROC curve into one number to compare models easily.

Use ROC and AUC to evaluate and improve classification models.

Practice

1. What does the ROC curve primarily show in a classification model?

easy

A. The trade-off between true positive rate and false positive rate at different thresholds

B. The accuracy of the model on the training data

C. The number of correct predictions made by the model

D. The loss value during model training

Solution

1. Step 1: Understand ROC curve components

   The ROC curve plots the true positive rate (sensitivity) against the false positive rate (1 - specificity) at various threshold settings.

2. Step 2: Identify what ROC shows

   This curve shows how well the model can distinguish between classes by varying the decision threshold.

3. Final Answer:

   The trade-off between true positive rate and false positive rate at different thresholds -> Option A

4. Quick Check:

   ROC curve = True Positive Rate vs False Positive Rate [OK]

Hint: ROC curve plots TPR vs FPR at thresholds [OK]

Common Mistakes:

• Confusing ROC with accuracy
• Thinking ROC shows loss values
• Assuming ROC shows only one threshold

2. Which of the following Python code snippets correctly imports the function to compute AUC from sklearn?

easy

A. import roc_auc_score from sklearn.metrics

B. from sklearn.metrics import auc_roc_score

C. from sklearn.metrics import roc_auc_score

D. import sklearn.metrics.roc_auc_score

Solution

1. Step 1: Recall correct import syntax

   In Python, functions are imported using 'from module import function' syntax.

2. Step 2: Identify correct function name

   The correct function name to compute AUC is 'roc_auc_score' from 'sklearn.metrics'.

3. Final Answer:

   from sklearn.metrics import roc_auc_score -> Option C

4. Quick Check:

   Correct import syntax = from sklearn.metrics import roc_auc_score [OK]

Hint: Use 'from sklearn.metrics import roc_auc_score' [OK]

Common Mistakes:

• Using wrong import syntax
• Misspelling function name
• Trying to import module as function

3. Given the following code, what is the printed AUC value?

from sklearn.metrics import roc_auc_score
true_labels = [0, 0, 1, 1]
predicted_scores = [0.1, 0.4, 0.35, 0.8]
auc = roc_auc_score(true_labels, predicted_scores)
print(round(auc, 2))

medium

A. 0.75

B. 0.85

C. 0.65

D. 0.95

Solution

1. Step 1: Understand roc_auc_score calculation

   The AUC measures how well the predicted scores rank positive samples higher than negative ones.

2. Step 2: Calculate AUC for given data

   Using the pairs, the AUC is 0.75 as the positive samples are ranked correctly most of the time but not perfectly.

3. Final Answer:

   0.75 -> Option A

4. Quick Check:

   AUC for given scores = 0.75 [OK]

Hint: Use roc_auc_score to get AUC directly [OK]

Common Mistakes:

• Confusing AUC with accuracy
• Rounding incorrectly
• Mixing up true labels and scores

4. Identify the error in the following code that tries to plot an ROC curve:

from sklearn.metrics import roc_curve
fpr, tpr, thresholds = roc_curve(y_true, y_pred)
plt.plot(fpr, tpr)
plt.show()

medium

A. roc_curve function is not imported correctly

B. y_pred should be predicted probabilities, not class labels

C. plt.plot should use thresholds instead of fpr

D. Missing import statement for numpy

Solution

1. Step 1: Check input requirements for roc_curve

   The roc_curve function requires true labels and predicted scores or probabilities, not class labels.

2. Step 2: Identify the error in inputs

   Using predicted class labels instead of probabilities causes incorrect ROC curve calculation.

3. Final Answer:

   y_pred should be predicted probabilities, not class labels -> Option B

4. Quick Check:

   Use probabilities for roc_curve inputs [OK]

Hint: Use predicted probabilities, not labels, for roc_curve [OK]

Common Mistakes:

• Passing class labels instead of probabilities
• Forgetting to import matplotlib.pyplot as plt
• Plotting thresholds instead of FPR and TPR

5. You have two models with these AUC scores: Model A = 0.82, Model B = 0.79. You want to improve Model B's performance. Which approach is best to increase the AUC score?

hard

A. Reduce the size of the training dataset to avoid overfitting

B. Tune the classification threshold to balance true positive and false positive rates

C. Use accuracy as the main metric instead of AUC

D. Increase the number of training epochs without changing data or model

Solution

1. Step 1: Understand what affects AUC

   AUC measures the model's ranking ability and is threshold-independent.

2. Step 2: Choose the best method to improve AUC

   Tuning the classification threshold does not improve AUC because AUC is threshold-independent; instead, improving the model's discriminative ability or training is needed.

3. Step 3: Evaluate options

   Increasing training epochs (Increase the number of training epochs without changing data or model) can help but may cause overfitting if not managed properly. Reducing dataset size (Reduce the size of the training dataset to avoid overfitting) usually harms performance. Using accuracy (Use accuracy as the main metric instead of AUC) does not improve AUC. Tuning threshold (Tune the classification threshold to balance true positive and false positive rates) affects operating point but not AUC.

4. Final Answer:

   Increase the number of training epochs without changing data or model -> Option D

5. Quick Check:

   More epochs can improve model performance and AUC [OK]

Hint: More training epochs improve AUC [OK]

Common Mistakes:

• Thinking threshold tuning affects AUC
• Reducing data size harms performance
• Switching to accuracy doesn't improve AUC