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Hinge Loss

Compute the hinge loss for SVM classification.

Given true labels $y_i \in \{-1, +1\}$ and raw predictions (scores) $\hat{y}_i$ :

$L = \frac{1}{n}\sum_{i=1}^{n} \max(0, 1 - y_i \cdot \hat{y}_i)$

This is the loss function used by Support Vector Machines. Points correctly classified with margin $\geq 1$ contribute zero loss.

Return the average hinge loss rounded to 4 decimal places.

Input:

y_true = [1, -1, 1, -1]
y_scores = [0.8, -1.2, 0.3, -0.5]

Output:

0.35

Reasoning:

First, we calculate the hinge loss for each sample:
- For $y_i = 1$ and $\hat{y}_i = 0.8$ , the loss is $\max(0, 1 - 1 \cdot 0.8) = \max(0, 0.2) = 0.2$
- For $y_i = -1$ and $\hat{y}_i = -1.2$ , the loss is $\max(0, 1 - (-1) \cdot (-1.2)) = \max(0, 1 - 1.2) = \max(0, -0.2) = 0$
- For $y_i = 1$ and $\hat{y}_i = 0.3$ , the loss is $\max(0, 1 - 1 \cdot 0.3) = \max(0, 0.7) = 0.7$
- For $y_i = -1$ and $\hat{y}_i = -0.5$ , the loss is $\max(0, 1 - (-1) \cdot (-0.5)) = \max(0, 1 - 0.5) = \max(0, 0.5) = 0.5$
Then, we calculate the average hinge loss: $L = \frac{1}{n}\sum_{i=1}^{n} \max(0, 1 - y_i \cdot \hat{y}_i) = \frac{1}{4}(0.2 + 0 + 0.7 + 0.5) = \frac{1.4}{4} = 0.35$
The final output is $0.35$

Editor

Python 3.13.1

0/0

Run code to see test results.

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