MAPE - Mean Absolute Percentage Error

The Mean Absolute Percentage Error (MAPE) [7] is a widely used statistical measure of prediction accuracy in forecasting, business, and economics.

Mathematically, it is the Mean Relative Error (MRE) multiplied by 100 to express the error as a percentage. It measures the average magnitude of the error relative to the actual value.

\[\text{MAPE}(y, \hat{y}) = \frac{100\%}{N} \sum_{i=1}^{N} \frac{|y_i - \hat{y}_i|}{|y_i|}\]

Description

Advantages:

  • Ultimate Interpretability: MAPE is arguably the most intuitive metric for non-technical stakeholders (e.g., management, clients). Stating “the model has a 5% error rate” is universally understood, whereas stating “the model has an RMSE of 12.4” requires deep domain context.

  • Scale-Independence: Because it is a percentage, you can use MAPE to compare the performance of models across different datasets, varying scales, or different product lines (e.g., predicting sales for a $10 item vs. a $1000 item).

Disadvantages:

  • The Zero-Value Trap (Critical Flaw): Just like MRE, if the actual ground truth value (\(y_i\)) is exactly 0.0, the calculation involves division by zero and will crash or return an infinite value. It cannot be used directly on intermittent demand datasets with zero-sales days.

  • Asymmetric Penalization (Hidden Bias): MAPE implicitly favors models that under-predict rather than over-predict. For example, if the actual value is 100 and the model predicts 50 (under-prediction by 50), the MAPE is 50%. However, if the model predicts 150 (over-prediction by 50), the MAPE is also 50%. But consider extreme cases: an under-prediction is bounded (you can’t predict less than 0, so max error is 100%), while an over-prediction has no upper bound (predicting 400 for a target of 100 yields a 300% error). This often forces models trained on MAPE to systematically under-forecast.

Properties

Example Usage

Note: Ensure your ground truth data does not contain zero values to avoid division-by-zero errors. Data should ideally be strictly positive.

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, 0.6, 2, 8])

evaluator = RegressionMetric(y_true, y_pred)
# Calculate Mean Absolute Percentage Error
print("MAPE: ", evaluator.MAPE())

## 2. For > 1-D array (Multi-output)
y_true = array([[0.5, 1], [0.1, 1], [7, 6]])
y_pred = array([[0.6, 2], [0.1, 2], [8, 5]])

evaluator = RegressionMetric(y_true, y_pred)
# Return an array of scores for each column
print("MAPE (Multi-output): ", evaluator.MAPE(multi_output="raw_values"))