What is the index of Regression algorithm?

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There are three commonly used Regression algorithm indexes: mean absolute error (Mean Absolute Error), mean square error (Mean Squared Error) and root mean square error (Root Mean Squared Error).

Mean absolute error (Mean Absolute Error)

From a geometric point of view, the average absolute error (Mean Absolute Error, MAE) represents the average distance between the predicted value and the actual value.

Its formula is as follows:

The evaluation index of average absolute error (Mean Absolute Error) is intuitive and easy to understand, but because there is an absolute value in the formula, the function is not smooth and can not be derived at some points. As an improvement, we can change the absolute value to the square of the average distance, that is, the mean square error (Mean Squared Error).

Mean square error (Mean Squared Error)

Mean Squared Error (MSE) can be regarded as the square of the average distance between the predicted value and the actual value in a geometric sense.

Its formula is as follows:

The mean square error (Mean Squared Error) solves the problem that the mean absolute error (Mean Absolute Error) can not be derived, but its size and the target variable are not on the same scale (different dimensions). In order to solve this problem, we can square the result of the mean square error (Mean Squared Error) and get the root mean square error.

Root mean square error (Root Mean Squared Error)

The root mean square error (Root Mean Squared Error, referred to as RMSE) is the result obtained by the square of the mean square error (Mean Squared Error), which solves the problem that the mean square error (Mean Squared Error) is inconsistent with the dimension of the target variable.

Its formula is as follows:

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