Shell Theory: A Statistical Model of Reality.

Area of Science:

• Machine Learning
• Statistical Modeling
• Data Science

Background:

• Machine learning relies on data separability, a concept difficult to formalize mathematically.
• Existing statistical methods struggle with high-dimensional data, often treating it as a degenerate case.

Purpose of the Study:

• To develop a robust statistical framework for machine learning in high-dimensional spaces.
• To address the mathematical challenges in formulating separability constraints for complex datasets.

Main Methods:

• Developed a novel statistical framework based on hierarchical generative processes for high-dimensional object representations.
• Introduced a distance-based statistical technique to analyze these generative processes.

Main Results:

• Demonstrated that instances within hierarchical generative processes are encapsulated by distinctive 'shells'.
• These shells effectively exclude instances from other processes, providing a formal basis for separability.
• Established 'shell theory' as a machine learning framework where separability is derived from generative assumptions.

Conclusions:

• Shell theory offers a mathematically rigorous approach to data separability in high dimensions.
• The framework leverages hierarchical structures and distinctive shells for improved machine learning model performance.
• This work bridges the gap between statistical theory and practical machine learning challenges in high-dimensional data analysis.