Codiscovering graphical structure and functional relationships within data: A Gaussian Process framework for...

Area of Science:

• Computational mathematics
• Machine learning
• Graph theory

Background:

• Scientific problems often involve function approximation across three complexity levels.
• Hypergraphs provide a framework for organizing computational knowledge.
• Type 3 problems require discovering hypergraph structure and approximating functions simultaneously.

Purpose of the Study:

• To introduce an interpretable Gaussian Process (GP) framework for Type 3 problems.
• To address the challenge of discovering unknown hypergraph structures from partial observations.
• To provide an efficient alternative to existing causal inference methods.

Main Methods:

• Utilizing Gaussian Processes (GPs) as a sensing mechanism.
• Leveraging nonlinear ANOVA capabilities of GPs.
• Developing a framework with polynomial complexity.

Main Results:

• The proposed GP framework enables data-driven discovery of hypergraph structure.
• It efficiently approximates unknown variables and functions without data randomization or sparsity assumptions.
• Achieves polynomial complexity, outperforming super-exponential complexity of causal inference methods.

Conclusions:

• The interpretable GP framework offers a powerful approach for complex computational knowledge discovery.
• This method advances the ability to model and analyze systems with unknown underlying structures.
• It provides a computationally efficient solution for problems involving hypergraph structure learning.