evalMet: Composite Evaluation Metric

The evalMet function computes the Evaluation Metric (EvalMet), a composite score that combines three robust criteria—Robust R-squared (RobR2), Geometric Mean of Model Fit Error (GMMFE), and Divergence Information (DivI)—to provide a comprehensive assessment of model performance.

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Overview

EvalMet is designed to quantify the overall quality of a model fit by integrating three complementary metrics:

• RobR2: Measures the proportion of variance explained by the model, robust to outliers.
• GMMFE: Captures the average multiplicative fitting error on a logarithmic scale.
• DivI: Quantifies the divergence in information content between the observed data and the model fit.

The combined metric is calculated as:

\[ \text{EvalMet} = \frac{\text{RobR2}}{\text{GMMFE} \cdot \text{DivI}} \]

A higher EvalMet value indicates a better model fit, balancing explained variance, error magnitude, and information divergence.

• Compatibility: Accepts NumPy arrays and Pandas Series for y, y_fit, and w.

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Parameters

Parameter	Type	Default	Description
y	array-like or Pandas Series	—	Observed data (ground truth). 1D values.
y_fit	array-like or Pandas Series	—	Fitted data (model predictions). 1D values, same shape as y.
w	array-like or Pandas Series	None	Optional weights for data points. 1D values, same shape as y. If not provided, equal weights are used.
verbose	bool	Print detailed progress, warnings, and results

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Returns

• float The computed Evaluation Metric (EvalMet) value.

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Raises

• ValueError
• If y and y_fit do not have the same shape.
• If w is provided and does not have the same shape as y.
• If y or y_fit are not 1D arrays.

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Example Usage

import numpy as np
from machinegnostics.metrics import evalMet

y = np.array([1.0, 2.0, 3.0, 4.0])
y_fit = np.array([1.1, 1.9, 3.2, 3.8])
result = evalMet(y, y_fit)
print(result)

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Notes

• EvalMet is most informative when used to compare multiple models or methods on the same dataset.
• The metric is robust to outliers and non-Gaussian data due to its use of gnostic algebra.
• EvalMet is especially useful in benchmarking and model selection scenarios, as it integrates multiple aspects of fit quality into a single score.

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Author: Nirmal Parmar
Date: 2025-09-24

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