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hc: Gnostic Characteristics (Hc) Metric

The hc function computes the Gnostic Characteristics (Hc) metric, a robust measure for evaluating the relevance or irrelevance between true and predicted values. Here, c denotes case of i- Estimation or j - Quantification condition. This metric is part of the Machine Gnostics framework and is particularly useful for assessing model performance in the presence of noise or outliers.

Overview

The Hc metric quantifies the relationship between predicted and true values using gnostic algebra. It can be used in two modes:

  • Relevance (case='i'): Measures how relevant the predictions are to the true values as per mathematical gnostics.
  • Irrelevance (case='j'): Measures how irrelevant the predictions are to the true values as per mathematical gnostics.

The metric is calculated as the normalized sum of squared gnostic characteristics, providing a robust alternative to classical error metrics.

Parameters

Parameter Type Default Description
y_true array-like — True (ground truth) values.
y_pred array-like — Predicted values from the model.
case str 'i' Calculation mode:'i' for relevance, 'j' for irrelevance.

Returns

  • float The calculated Hc value (normalized sum of squared gnostic characteristics).

Raises

  • ValueError
  • If y_true and y_pred have different lengths.
  • If case is not 'i' or 'j'.

Example Usage

from machinegnostics.metrics import hc

y_true = [1, 2, 3]
y_pred = [1, 2, 3]

# Calculate gnostic relevance
hc_value = hc(y_true, y_pred, case='i')
print(hc_value)

Notes

  • The function uses the GnosticsCharacteristics class from the Machine Gnostics library.
  • The ratio \(R = y_{\text{true}} / y_{\text{pred}}\) is used to compute the gnostic characteristics.
  • The result is normalized by the number of samples.
  • Use case='i' for relevance and case='j' for irrelevance, depending on your analysis needs.