A10 - A10 Index

The A10 Index is a strictly threshold-based regression metric widely used in engineering and empirical models. It quantifies the proportion of predictions that deviate by no more than ±10% from the actual ground truth values.

\[\begin{split}\text{A10}(y, \hat{y}) = \frac{1}{N} \sum_{i=1}^{N} \begin{cases} 1, & \text{if } \frac{|y_i - \hat{y}_i|}{|y_i|} \leq 0.1 \\ 0, & \text{otherwise} \end{cases}\end{split}\]

Description

Advantages:

  • Exceptional interpretability: Directly translates into business, engineering, or clinical success criteria (e.g., “85% of our predictions fall within the strict 10% margin of error”).

  • Robust to extreme outliers: Unlike RMSE or MSE, massive prediction errors do not disproportionately skew the final score. An outlier is simply counted as a failure (score = 0).

Disadvantages:

  • Rigid threshold (Cliff effect): A prediction with a 10.1% error is penalized exactly the same as a prediction with a 500% error. It completely ignores “near-misses”.

  • Undefined for zero targets: Because it divides by the actual value (\(y_i\)), the metric calculation will crash or become undefined if the ground truth data contains absolute zeros.

Properties

  • Best possible score: 1.0 (Higher is better, meaning 100% of samples are within the ±10% tolerance zone).

  • Range: [0.0, 1.0]

  • Mathematical Reference: MDPI Applied Sciences

Example Usage

from numpy import array
from permetrics.regression import RegressionMetric

## 1. For 1-D array (Single-output)
y_true = array([3, -0.5, 2, 7])
y_pred = array([2.5, 0.0, 2, 8])

evaluator = RegressionMetric(y_true, y_pred)
# Calculate A10 Index
print("A10 Index: ", evaluator.A10())

## 2. For > 1-D array (Multi-output)
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)
# Return an array of scores for each column
print("A10 Index (Multi-output): ", evaluator.A10(multi_output="raw_values"))