Towards a Kernel based Physical Interpretation of Model Uncertainty

This paper introduces a new information theoretic framework that provides a sensitive multi-modal quantification of time series uncertainty by leveraging a quantum physical description of the projected feature space in a Reproducing Kernel Hilbert Space (RKHS). We specifically modify the kernel mean embedding, which yields an intuitive physical interpretation of the signal structure, to produce a dynamic potential field, resulting in a new energy based formulation that exploits the mathematics of quantum theory. This enables one to extract multi-scale uncertainty features of the time series in the form of information eigenmodes by utilizing moment decomposition concepts of quantum physics. In essence, this approach decomposes local time realizations of the stochastic joint process PDF in terms of quantum uncertainty moments. We specifically present the application of this framework as a non-parametric and non-intrusive surrogate tool for predictive uncertainty quantification of point-prediction neural network models, overcoming various limitations of conventional Bayesian and ensemble based UQ methods. Experimental comparisons with some established uncertainty quantification methods illustrate performance advantages exhibited by our framework.