Beginner

Compute Mean Squared Error

Beginner

~8 min

code completion

Mean Squared Error Loss

Before we can optimize a model, we need to measure how wrong it is. Mean Squared Error (MSE) is the most common loss function for regression:

MSE = \frac{1}{n} i = 1 \sum n (y_{i} - \overset{y}{^}_{i})^{2}

where $y_{i}$ are the true labels and $\overset{y}{^}_{i}$ are the predictions.

Properties of MSE:

Always non-negative (minimum is 0, perfect predictions)

Penalizes large errors heavily (squared)

Differentiable everywhere (important for gradient descent)

Your task: Implement mean_squared_error(y_true, y_pred) using NumPy. Do not use a for loop.

Example Tests

Perfect predictions → MSE = 0

Input: {"y_pred":[1,2,3],"y_true":[1,2,3]}

Expected: 0

Known MSE value

Input: {"y_pred":[2,2,2,2],"y_true":[1,2,3,4]}

Expected: 1.5

Single element

Input: {"y_pred":[3],"y_true":[5]}

Expected: 4

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