Sensitivity Score for Binary Classifier

Easy

In the realm of machine learning evaluation, sensitivity (also known as the true positive rate or hit rate) stands as one of the most critical metrics for assessing how well a classifier captures positive instances. This metric answers a fundamental question: "Of all the samples that are actually positive, what fraction did our model correctly identify?" Sensitivity is formally defined as: $$\text{Sensitivity} = \frac{TP}{TP + FN}$$ Where: TP (True Positives): The number of positive samples correctly predicted as positive FN (False Negatives): The number of positive samples incorrectly predicted as negative Intuitive Understanding: Imagine a medical screening test designed to detect a disease. A sensitivity of 0.95 means that out of every 100 people who actually have the disease, the test correctly identifies 95 of them. The remaining 5 are "missed" (false negatives). In high-stakes scenarios like cancer detection or fraud prevention, maximizing sensitivity is often crucial because missing a true positive can have severe consequences. The Trade-off Consideration: While high sensitivity is desirable, it often comes at the cost of increased false positives. A model that predicts everything as positive would achieve perfect sensitivity (1.0) but would be practically useless. Understanding this trade-off is essential for building effective classifiers. Your Task: Implement a function that computes the sensitivity score for a binary classification model. The function should: Accept two lists: the actual ground truth labels and the predicted labels Return the sensitivity value rounded to three decimal places Handle the edge case where there are no actual positive samples by returning 0.0 (to prevent division by zero)

Example 1

Input

actual_labels = [1, 0, 1, 1, 0, 1]
predicted_labels = [1, 0, 1, 0, 0, 1]

Output

0.75

Explanation

Let's identify the components: • Total actual positives (1s in actual_labels): 4 instances (positions 0, 2, 3, 5) • True Positives: Positions where actual=1 AND predicted=1: positions 0, 2, 5 → 3 instances • False Negatives: Positions where actual=1 AND predicted=0: position 3 → 1 instance Sensitivity = TP / (TP + FN) = 3 / (3 + 1) = 3/4 = 0.75 The model successfully identified 75% of all positive cases.

Example 2

Input

actual_labels = [1, 1, 1, 0, 0]
predicted_labels = [1, 1, 1, 0, 1]

Output

1.0

Explanation

Analyzing the classification: • Total actual positives: 3 instances (positions 0, 1, 2) • True Positives: All 3 actual positives were correctly predicted → 3 instances • False Negatives: No positive samples were missed → 0 instances Sensitivity = 3 / (3 + 0) = 1.0 Perfect sensitivity! The model captured ALL positive cases. Note: There is one false positive at position 4 (predicted=1, actual=0), but this doesn't affect sensitivity—it would affect precision instead.

Example 3

Input

actual_labels = [1, 1, 1, 0, 0]
predicted_labels = [0, 0, 0, 1, 1]

Output

0.0

Explanation

This represents the worst-case scenario: • Total actual positives: 3 instances (positions 0, 1, 2) • True Positives: None of the actual positives were correctly identified → 0 instances • False Negatives: All 3 positive samples were missed → 3 instances Sensitivity = 0 / (0 + 3) = 0.0 The model failed to identify ANY positive cases. Interestingly, the model also predicted all negatives as positives, suggesting the predictions might be inverted or the model is fundamentally flawed.

Constraints

1 ≤ length of actual_labels ≤ 10,000
actual_labels and predicted_labels have the same length
Each element in both lists is either 0 or 1
The lists represent binary classification outcomes only

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Sensitivity Score for Binary Classifier

Easy

In the realm of machine learning evaluation, sensitivity (also known as the true positive rate or hit rate) stands as one of the most critical metrics for assessing how well a classifier captures positive instances. This metric answers a fundamental question: "Of all the samples that are actually positive, what fraction did our model correctly identify?" Sensitivity is formally defined as: $$\text{Sensitivity} = \frac{TP}{TP + FN}$$ Where: TP (True Positives): The number of positive samples correctly predicted as positive FN (False Negatives): The number of positive samples incorrectly predicted as negative Intuitive Understanding: Imagine a medical screening test designed to detect a disease. A sensitivity of 0.95 means that out of every 100 people who actually have the disease, the test correctly identifies 95 of them. The remaining 5 are "missed" (false negatives). In high-stakes scenarios like cancer detection or fraud prevention, maximizing sensitivity is often crucial because missing a true positive can have severe consequences. The Trade-off Consideration: While high sensitivity is desirable, it often comes at the cost of increased false positives. A model that predicts everything as positive would achieve perfect sensitivity (1.0) but would be practically useless. Understanding this trade-off is essential for building effective classifiers. Your Task: Implement a function that computes the sensitivity score for a binary classification model. The function should: Accept two lists: the actual ground truth labels and the predicted labels Return the sensitivity value rounded to three decimal places Handle the edge case where there are no actual positive samples by returning 0.0 (to prevent division by zero)

Example 1

Input

actual_labels = [1, 0, 1, 1, 0, 1]
predicted_labels = [1, 0, 1, 0, 0, 1]

Output

0.75

Explanation

Example 2

Input

actual_labels = [1, 1, 1, 0, 0]
predicted_labels = [1, 1, 1, 0, 1]

Output

1.0

Explanation

Example 3

Input

actual_labels = [1, 1, 1, 0, 0]
predicted_labels = [0, 0, 0, 1, 1]

Output

0.0

Explanation

Constraints

1 ≤ length of actual_labels ≤ 10,000
actual_labels and predicted_labels have the same length
Each element in both lists is either 0 or 1
The lists represent binary classification outcomes only