Mean Square Error

Used for regression tasks, where the target variable is continuous (e.g. house price, temperature, stock value).

$$ MSE = \frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2 $$

• \(n\) = number of samples
• \(y_i\) = true (ground-truth) value
• \(\hat{y}_i\) = predicted value

Interpretation:

• Measures the average squared difference between predicted and true values.
• Squaring penalizes large errors more strongly than small ones.
• The loss is always non-negative and equals 0 only when predictions are perfect.

Properties:

• Differentiable and smooth → works well with gradient-based optimization.
• Sensitive to outliers due to the squared term.
• Assumes errors are normally distributed (underlying statistical interpretation).