Mean-squared error (MSE) loss is defined as:

$$ \cal L_\text{MSE}(y,\hat y)=\frac1n\sum^n_{i=1}(y_i-\hat y_i)^2 $$

• Assumes Gaussian noise
• Equivalent is maximum likelihood under $\epsilon\sim\cal N(0,\sigma^2)$

References

Loss function

Maximum likelihood estimation (MLE)