  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.
