Regression Metrics' Guide - Open Source Leader in AI and ML

The target's distribution is right skewed with some fairly high values compared to the mean: The Root Mean Squared Error (RMSE) or Mean Squared Error (MSE, which is basically the same as RMSE without the squared root) is the most popular regression metric. If there was a king/queen of regression metrics, this would have been it! Where y i is the prediction and yi the actual target value. In other words, you square all the errors (or residuals as they call them) per sample/row, then sum them, divide by the total number of observations and take the squared root to bring the metric back to the original space (or you don't in MSE). It is also one of the oldest regression metrics. Smaller errors (that are for example less than 1.) will have an even lower contribution to the overall error after being squared, whereas bigger errors will have much more weight after being squared. A large error in a given sample can have huge impact on the overall results and make an optimizer focus on reducing the error for that single sample, making the prediction for every other sample worse. This is because of the "squared" attribute, it makes it easily differentiable, something that gradient-based algorithms (like Stochastic Gradient Descent) can leverage.