Mean squared error

Mean squared error is one of the most common regression cost functions. Its generic expression is:

This function is differentiable at every point of its domain and it's convex, so it can be optimized using the stochastic gradient descent (SGD) algorithm; however, there's a drawback when employed in regressions where there are outliers. As its value is always quadratic when the distance between the prediction and the actual value (corresponding to an outlier) is large, the relative error is high, and this can lead to an unacceptable correction.