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.

---

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.

---

Parameters

Parameter	Type	Default	Description
y	np.ndarray	—	Observed data (ground truth). 1D array of numerical values.
y_fit	np.ndarray	—	Fitted data (model predictions). 1D array, same shape as y.
w	np.ndarray	None	Optional weights for data points. 1D array, same shape as y. If not provided, equal weights are used.

---

Returns

• float The computed Evaluation Metric (EvalMet) value.

---

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.

---

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)

---

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.

---