Toward a Kernel-Based Uncertainty Decomposition Framework for Data and Models.

Area of Science:

• Computational statistics
• Machine learning theory
• Quantum mechanics applications

Background:

• Predictive uncertainty quantification is crucial for reliable AI models.
• Existing Bayesian methods face limitations in complex scenarios.
• New approaches are needed for robust uncertainty estimation.

Purpose of the Study:

• Introduce a new framework for quantifying predictive uncertainty in data and models.
• Develop a method that overcomes limitations of conventional Bayesian approaches.
• Enhance the discriminative resolution of epistemic uncertainty in data.

Main Methods:

• Projecting data into a Gaussian reproducing kernel Hilbert space (RKHS).
• Transforming probability density functions (PDFs) to quantify gradient flow as a topological potential field.
• Decomposing PDF gradient flow using quantum physics operators (Schrödinger's formulation) and moment decomposition.

Main Results:

• Higher-order moments systematically cluster PDF tail regions, improving uncertainty resolution.
• The framework effectively decomposes local PDF realizations into uncertainty moments.
• Demonstrated superior performance compared to established uncertainty quantification methods.

Conclusions:

• The proposed framework offers a powerful new tool for predictive uncertainty quantification.
• It provides enhanced discriminative resolution of epistemic uncertainty.
• The method shows significant advantages over traditional Bayesian-based techniques for neural network models.