EVS - Explained Variance Score
\[EVS = 1 - \frac{Var\{ y_{true} - y_{pred} \}}{Var \{ y_{true} \} }\]
The given math formula defines the explained variance score (EVS) [1], which is a metric used in regression analysis to evaluate the performance of a model. The formula computes the ratio of the variance of the difference between the true values y_true and the predicted values y_pred to the variance of the true values y_true.
The resulting score ranges between -infinity and 1, with a score of 1 indicating a perfect match between the true and predicted values and a score of 0 indicating that the model does not perform better than predicting the mean of the true values.
A higher value of EVS indicates a better performance of the model. Best possible score is 1.0, greater values are better. Range = (-inf, 1.0].
Example to use EVS metric:
from numpy import array
from permetrics.regression import RegressionMetric
## For 1-D array
y_true = array([3, -0.5, 2, 7])
y_pred = array([2.5, 0.0, 2, 8])
evaluator = RegressionMetric(y_true, y_pred)
print(evaluator.explained_variance_score())
## For > 1-D array
y_true = array([[0.5, 1], [-1, 1], [7, -6]])
y_pred = array([[0, 2], [-1, 2], [8, -5]])
evaluator = RegressionMetric(y_true, y_pred)
print(evaluator.EVS(multi_output="raw_values"))