VAF - Variance Accounted For

\[\text{VAF}(y, f_i) = 100\% \times \frac{\sum_{i=1}^{n}(y_i - \bar{y})(f_i - \bar{f})}{\sum_{i=1}^{n}(y_i - \bar{y})^2}\]

Latex equation code:

\text{VAF}(y, f_i) = 100\% \times \frac{\sum_{i=1}^{n}(y_i - \bar{y})(f_i - \bar{f})}{\sum_{i=1}^{n}(y_i - \bar{y})^2}

• Variance Accounted For (VAF) is a metric used to evaluate the performance of a regression model. It measures the proportion of the total variance in the

actual values that is accounted for by the variance in the predicted values. + Variance Accounted For between 2 signals (VAF): Best possible score is 100% (identical signal), bigger value is better. Range = (-inf, 100%] + Link to equation

Example to use VAF 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.variance_accounted_for())

## 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.VAF(multi_output="raw_values"))