WI - Willmott Index
\[\text{WI}(y, \hat{y}) = 1 - \frac{ \sum_{i=0}^{N - 1} (\hat{y_i} - y_i)^2 }{ \sum_{i=0}^{N - 1} (|\hat{y_i} - mean(y)| + |y_i - mean(y)|)^2}\]
Willmott Index (WI): Best possible score is 1.0, bigger value is better. Range = [0, 1]
Reference evapotranspiration for Londrina, Paraná, Brazil: performance of different estimation methods
Latex equation code:
\text{WI}(y, \hat{y}) = 1 - \frac{ \sum_{i=0}^{N - 1} (\hat{y_i} - y_i)^2 }{ \sum_{i=0}^{N - 1} (|\hat{y_i} - mean(y)| + |y_i - mean(y)|)^2}
Example to use WI 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, decimal=5)
print(evaluator.willmott_index())
## 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, decimal=5)
print(evaluator.WI(multi_output="raw_values"))