On the Conditions for Domain Stability for Machine Learning: a Mathematical Approach

TL;DR

This paper introduces a mathematical framework for understanding and verifying the stability of machine learning models, linking it to topological and metric properties of their domains and classification sets.

Contribution

It defines a formal property of stability for ML models and provides conditions and equivalences to test and prove this stability using topological and metric space theory.

Findings

Stability relates to function smoothness and topological properties.

Sufficient conditions for stability are established.

Provides methods to test and validate model stability.

Abstract

This work proposes a mathematical approach that (re)defines a property of Machine Learning models named stability and determines sufficient conditions to validate it. Machine Learning models are represented as functions, and the characteristics in scope depend upon the domain of the function, what allows us to adopt topological and metric spaces theory as a basis. Finally, this work provides some equivalences useful to prove and test stability in Machine Learning models. The results suggest that whenever stability is aligned with the notion of function smoothness, then the stability of Machine Learning models primarily depends upon certain topological, measurable properties of the classification sets within the ML model domain.