MASE - Mean Absolute Scaled Error
\[\text{MASE}(y, \hat{y}) = \frac{ \frac{1}{N} \sum_{i=0}{N-1} |y_i - \hat{y_i}| }{ \frac{1}{N-1} \sum_{i=1}^{N-1} |y_i - y_{i-1}| }\]
Latex equation code:
\text{MASE}(y, \hat{y}) = \frac{ \frac{1}{N} \sum_{i=0}{N-1} |y_i - \hat{y_i}| }{ \frac{1}{N-1} \sum_{i=1}^{N-1} |y_i - y_{i-1}| }
Best possible score is 0.0, smaller value is better. Range = [0, +inf)
m = 1 for non-seasonal data, m > 1 for seasonal data
Example to use MASE 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.mean_absolute_scaled_error())
## 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.MASE(multi_output="raw_values"))