Glossary¶

Abstract

This document provides definitions and explanations for the main arguments and variables used in Machine Gnostics data analytics, machine learning, and deep learning models. Understanding these concepts will help users grasp the unique characteristics of the Machine Gnostics library, which is based on the non-statistical paradigm of Mathematical Gnostics.

Core Concepts¶

Machine Gnostics: A machine learning and deep learning library founded on Mathematical Gnostics, a non-statistical paradigm for data analysis.
Mathematical Gnostics: An alternative to traditional statistical methods, focusing on the quantification and estimation of uncertainty in data.

Key Arguments and Gnostic Characteristics¶

1. Gnostic Geometries¶

These are the fundamental variables used to describe data in the gnostic framework. They are divided into two main spaces:

Quantifying Space (Q-space, \( j \)): Describes the variability and irrelevance in the data.
Estimating Space (E-space, \( i \)): Describes the estimation of variability and relevance.

Comparative Table of Geometries:

Feature	Quantifying (Q-space)	Estimating (E-space)
Variability	\( f_j \) (Quantifying data variability)	\( f_i \) (Estimating data variability)
Relevance/Irrelevance	\( h_j \) (Quantifying irrelevance/error)	\( h_i \) (Estimating relevance)
Probability	\( p_j \) (Quantifying probability)	\( p_i \) (Estimating probability)
Information	\( I_j \) (Quantifying information)	\( I_i \) (Estimating information)
Entropy	\( e_j \) (Quantifying entropy)	\( e_i \) (Estimating entropy)

All four key variables (\( f_j, h_j, f_i, h_i \)) are collectively called gnostic characteristics.

Detailed Definitions¶

2. Entropy & Residuals¶

\( e_i \): Estimating entropy
Entropy estimate for the data.
\( e_j \): Quantifying entropy
Quantifies the entropy content.
\( re \): Residual entropy
The remaining entropy after estimation, representing the difference between quantification and estimation entropy.

3. Loss Functions¶

\( H_c \) loss: Gnostic mean relevance loss
A loss function based on gnostic relevance, where \( c \) can be \( i \) or \( j \).