Towards a Kernel based Uncertainty Decomposition Framework for Data and Models
This work addresses uncertainty quantification in machine learning, offering a novel decomposition approach that could improve reliability in applications like risk assessment, though it appears incremental as it builds on kernel methods and quantum physics operators.
The paper tackles predictive uncertainty quantification for data and models by introducing a kernel-based framework that decomposes the probability density function gradient flow into uncertainty moments, showing that higher-order modes cluster tail regions to resolve epistemic uncertainty. It applies this as a surrogate tool for neural networks, overcoming limitations of Bayesian methods and demonstrating performance advantages in experiments.
This paper introduces a new framework for quantifying predictive uncertainty for both data and models that relies on projecting the data into a Gaussian reproducing kernel Hilbert space (RKHS) and transforming the data probability density function (PDF) in a way that quantifies the flow of its gradient as a topological potential field quantified at all points in the sample space. This enables the decomposition of the PDF gradient flow by formulating it as a moment decomposition problem using operators from quantum physics, specifically the Schrodinger's formulation. We experimentally show that the higher order modes systematically cluster the different tail regions of the PDF, thereby providing unprecedented discriminative resolution of data regions having high epistemic uncertainty. In essence, this approach decomposes local realizations of the data PDF in terms of uncertainty moments. We apply this framework as a surrogate tool for predictive uncertainty quantification of point-prediction neural network models, overcoming various limitations of conventional Bayesian based uncertainty quantification methods. Experimental comparisons with some established methods illustrate performance advantages exhibited by our framework.