Probabilistic Perspective of Jungck Contractive Situations in Machine Learning

In the realm of machine learning (ML), the underlying mathematical frameworks significantly influence the development and efficacy of algorithms. One such framework is the probabilistic metric space, which provides a robust foundation for handling uncertainty and variability inherent in real-world problems and data. This work explores the applicability of probabilistic metric spaces in machine learning, with a particular focus on the Jungck contractive notion. The Jungck contraction theorem extends the classical Banach contraction principle to the setting of probabilistic metric spaces. This theorem is pivotal for proving the existence and uniqueness of fixed points in probabilistic settings, which is crucial for the convergence analysis of ML algorithms. This generalises invariant point propositions to probabilistic settings, offers powerful tools for the convergence analysis of iterative ML algorithms.