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This paper introduces a new framework for quantifying predictive uncertaintyfor both data and models that relies on projecting the data into a Gaussianreproducing kernel Hilbert space (RKHS) and transforming the data probabilitydensity function (PDF) in a way that quantifies the flow of its gradient as atopological potential field quantified at all points in the sample space. Thisenables the decomposition of the PDF gradient flow by formulating it as amoment decomposition problem using operators from quantum physics, specificallythe Schrodinger's formulation. We experimentally show that the higher ordermodes systematically cluster the different tail regions of the PDF, therebyproviding unprecedented discriminative resolution of data regions having highepistemic uncertainty. In essence, this approach decomposes local realizationsof the data PDF in terms of uncertainty moments. We apply this framework as asurrogate tool for predictive uncertainty quantification of point-predictionneural network models, overcoming various limitations of conventional Bayesianbased uncertainty quantification methods. Experimental comparisons with someestablished methods illustrate performance advantages exhibited by ourframework.

Towards a Kernel based Uncertainty Decomposition Framework for Data and Models