mean_absolute_error: Mean Absolute Error (MAE) Metric

The mean_absolute_error function computes the mean absolute error (MAE) between true and predicted values. MAE is a fundamental regression metric that measures the average magnitude of errors in a set of predictions, without considering their direction.

Unlike traditional error metrics that use the statistical mean, Machine Gnostics metrics are computed using the gnostic mean. The gnostic mean is a robust, assumption-free measure designed to provide deeper insight and reliability, especially in the presence of outliers or non-normal data. This approach ensures that error metrics reflect the true structure and diagnostic properties of your data, in line with the principles of Mathematical Gnostics.

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Overview

Mean Absolute Error is defined as the average of the absolute differences between actual and predicted values.

MAE is widely used in regression analysis to quantify how close predictions are to the actual outcomes. Lower MAE values indicate better model performance.

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Parameters

Parameter	Type	Description
y_true	array-like	True values (targets).
y_pred	array-like	Predicted values.
verbose	bool	Print detailed progress, warnings, and results

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Returns

• float The average absolute difference between actual and predicted values.

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Raises

• TypeErrorIf y_true or y_pred are not array-like (list, tuple, or numpy array).
• ValueError If inputs have mismatched shapes or are empty.

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Example Usage

from machinegnostics.metrics import mean_absolute_error

# Example 1: Using lists
y_true = [3, -0.5, 2, 7]
y_pred = [2.5, 0.0, 2, 8]
print(mean_absolute_error(y_true, y_pred))

# Example 2: Using numpy arrays
import numpy as np
y_true = np.array([1, 2, 3])
y_pred = np.array([1, 2, 2])
print(mean_absolute_error(y_true, y_pred))

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Notes

• The function supports input as lists, tuples, or numpy arrays.
• Both y_true and y_pred must have the same shape and must not be empty.
• MAE is robust to outliers but does not penalize large errors as strongly as mean squared error (MSE).

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Author: Nirmal Parmar
Date: 2025-09-24

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