🔬 Mean Squared Error (MSE)

Mean Squared Error (MSE)#

The average of squared differences between predictions and actuals.

Important

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What it is#

Mean squared error is the average of the squared differences between predictions and truth — the workhorse loss and metric for regression (also called L2 or quadratic loss):

\[\text{MSE} = \frac{1}{n}\sum_{i=1}^{n}\big(y_i - \hat{y}_i\big)^2.\]

Squaring makes every error positive and weights large errors far more than small ones.

How it behaves#

Because errors are squared, MSE is dominated by big misses and is sensitive to outliers — one large error can swamp many small ones. Its units are the square of the target’s, so it doesn’t read directly; minimizing MSE yields the mean (conditional expectation) as the optimal prediction.

Why it’s used#

It is smooth and differentiable, ideal for gradient descent (it is the loss regression networks minimize), and it is the maximum-likelihood loss under Gaussian noise. When outliers should count less, MAE is preferred.

Theme: Model Evaluation & Uncertainty · All terminology

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Mind map — connected ideas

Root Mean Squared Error (RMSE) · Mean Absolute Percentage Error (MAPE) · Loss Functions · R² (R-squared) · Regression Models · Forecast Error

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More in Model Evaluation & Uncertainty

Average Absolute Error (AAE) · Baseline Heuristics · Bootstrap · Bootstrap Confidence Intervals (CIs) · Coverage · Cramér’s V · DeLong’s Test · KS Statistic (Kolmogorov–Smirnov Statistic) · Likelihood Ratio (LR) · Mann–Whitney U Test (also called the Wilcoxon rank-sum test) · MASE (Mean Absolute Scaled Error) · Mean Absolute Error (MAE) · Mean Absolute Percentage Error (MAPE) · Relative accuracy