root_mean_squared_error: Root Mean Squared Error (RMSE) Metric

The root_mean_squared_error function computes the Root Mean Squared Error (RMSE) between true and predicted values. RMSE is a widely used regression metric that measures the square root of the average of the squared differences between predicted and actual values.

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

Root Mean Squared Error is defined as the square root of the mean squared error.

RMSE provides an interpretable measure of prediction error in the same units as the target variable. Lower RMSE 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 square root of the average of squared errors 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 root_mean_squared_error

# Example 1: Using lists
y_true = [3, -0.5, 2, 7]
y_pred = [2.5, 0.0, 2, 8]
print(root_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(root_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.
• RMSE is sensitive to outliers due to the squaring of errors.
• RMSE is in the same units as the target variable, making it easy to interpret.

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Author: Nirmal Parmar
Date: 2025-09-24

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