Machine Gnostics Measures

Note

Why Machine Gnostics?
Unlike classical statistics, which rely on probabilistic averages, Machine Gnostics computes measures like mean, median, standard deviation, and variance using irrelevance and fidelity from gnostic theory. This approach is assumption-free and robust to outliers, revealing the true diagnostic properties of your data.

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1. Sample Data

Let’s start with a small dataset that includes an outlier, to see how Machine Gnostics handles challenging real-world data.

Sample Data

import numpy as np

# Example data with an outlier
data = np.array([-13.5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
print("Data:", data)

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2. Gnostic Mean

The gnostic mean is robust to outliers and does not assume a specific data distribution.

Gnostic Mean

import machinegnostics as mg

mean = mg.mean(data)
print("Gnostic Mean:", mean)

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3. Gnostic Median

The gnostic median provides a robust central value, even for small or skewed samples.

Gnostic Median

import machinegnostics as mg

median = mg.median(data)
print("Gnostic Median:", median)

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4. Gnostic Standard Deviation

Unlike classical standard deviation, the gnostic version returns a lower and upper bound, reflecting uncertainty more realistically.

Gnostic Standard Deviation

import machinegnostics as mg

std_dev_lb, std_dev_ub = mg.std(data)
print("Gnostic Std Dev (lower, upper):", std_dev_lb, std_dev_ub)

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5. Gnostic Variance

Gnostic variance is always between 0 and 1, as it is calculated using irrelevance rather than squared deviations.

Gnostic Variance

import machinegnostics as mg

var = mg.variance(data)
print("Gnostic Variance:", var)

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Tips

• Robustness: Try changing or adding more outliers to your data and see how the gnostic measures respond compared to classical statistics.
• Integration: All functions follow standard Python/NumPy conventions and can be used in data science workflows.
• Documentation: See the API Reference for advanced options and parameter tuning.

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Next:
Explore more tutorials and real-world examples in the Examples section!