Mean Squared Error (MSE) is a common loss function for regression tasks and a measure of the quality of an estimator. It’s defined as the average of the squares of the differences between predicted values (\hat{y}) and actual values (y): MSE = (1/n) * Σ (y_i - \hat{y}_i)^2. Squaring the error amplifies larger errors (makes the loss more sensitive to outliers). MSE is differentiable, which is convenient for optimization (gradient is the mean of residuals times -2). The square root of MSE is the RMSE (Root Mean Squared Error), which is in the same unit as the original output (for interpretability). MSE is also related to variance: it can be decomposed into Bias^2 + Variance + noise^2 for an estimator. In model training, minimizing MSE leads to the optimal prediction being the mean of the target distribution (for a given input) if the data has Gaussian noise. While simple and widely used, MSE may not be ideal if outliers are prevalent (MAE might be better in those cases) or if one cares about relative vs absolute errors.