mean_squared_error: Mean Squared Error (MSE) Metric

The mean_squared_error function computes the mean squared error (MSE) between true and predicted values. MSE is a fundamental regression metric that measures the average of the squares of the errors—that is, the average squared difference between the estimated values and the actual value.

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 Squared Error is defined as the average of the squared differences between actual and predicted values.

MSE is widely used in regression analysis to quantify the accuracy of predictions. Lower MSE values indicate better model performance, while higher values indicate larger errors.

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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 of squared differences 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_squared_error

# Example 1: Using lists
y_true = [3, -0.5, 2, 7]
y_pred = [2.5, 0.0, 2, 8]
print(mean_squared_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_squared_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.
• MSE penalizes larger errors more than MAE (mean absolute error), making it sensitive to outliers.

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Author: Nirmal Parmar
Date: 2025-09-24

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