mean squared error

$$MSE=\frac{1}{n}\sum _{i=1}^n(Y_i-{\hat{Y}}_i{)}^2$$

Pytorch:

import torch.nn.functional as F
F.mse_loss(y_pred, y_target)
# smoothly switches from l1 to l2 loss for small differnces
F.smooth_l1_loss(y_pred, y_target)

Advantages to MAE:

• Emphasizes larger errors.
• Smoother (no .abs())

Disadvantages:

• Might not be as robust to outliers