A10 - A10 index

\[\begin{split}\text{A10}(y, \hat{y}) = \frac{1}{n}\sum_{i=1}^{n} \left\{\begin{array}{ll} 1, & \textrm{if } \frac{|\hat{y}_i - y_i|}{y_i} \leq 0.1\\ 0, & \textrm{otherwise} \end{array}\right.\end{split}\]

Latex equation code:

\text{A10}(y, \hat{y}) = \frac{1}{n}\sum_{i=1}^{n} \left\{\begin{array}{ll} 1, & \textrm{if } \frac{|\hat{y}_i - y_i|}{y_i} \leq 0.1\\ 0, & \textrm{otherwise} \end{array}\right.

• Best possible score is 1.0, bigger value is better. Range = [0, 1]

• a10-index is engineering index for evaluating artificial intelligence models by showing the number of samples that fit the

prediction values with a deviation of ±10% compared to experimental values + Link to equation

In other words, the A10 metric measures the proportion of cases where the absolute difference between the predicted and actual values is less than or equal to 10% of the actual value. A higher A10 score indicates better predictive accuracy, as the model is able to make more accurate predictions that are closer to the actual values.

Example to use A10 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.a10_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)
print(evaluator.A10(multi_output="raw_values"))