A30 - A30 Index

The A30 Index [15] is an empirical evaluation metric that quantifies the proportion of predictions falling within a ±30% deviation from the experimental (actual) values.

This metric is often utilized in highly variable domains or early-stage modeling where a wider tolerance margin (30%) is practically acceptable. A higher A30 score indicates better predictive accuracy, demonstrating that a larger percentage of the model’s predictions are close to the actual values.

\[\begin{split}\text{A30}(y, \hat{y}) = \frac{1}{N} \sum_{i=1}^{N} \begin{cases} 1, & \text{if } \frac{|y_i - \hat{y}_i|}{|y_i|} \leq 0.3 \\ 0, & \text{otherwise} \end{cases}\end{split}\]

Description

Advantages:

  • High interpretability: Easily understood by non-technical stakeholders (e.g., “85% of predictions are within a 30% error margin”).

  • Accommodates high variance: Extremely useful for datasets with inherent noise where stricter metrics (like A10) might fail to capture the model’s baseline utility.

  • Outlier resilience: Extreme deviations do not disproportionately skew the metric; they are simply counted as outside the tolerance threshold (score = 0).

Disadvantages:

  • Rigid threshold (Cliff effect): A prediction with a 30.1% error is penalized exactly the same as a prediction with a 500% error. It ignores the concept of “near-misses”.

  • Zero-target vulnerability: Because the formula divides by the actual value (\(y_i\)), the calculation will become undefined (division by zero) if the ground truth data contains absolute zeros.

Properties

  • Best possible score: 1.0 (Higher is better; 100% of samples fall within the ±30% tolerance zone).

  • Range: [0.0, 1.0]

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 A30 Index
print("A30 Index: ", evaluator.A30())

## 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("A30 Index (Multi-output): ", evaluator.A30(multi_output="raw_values"))