Log In Sign Up

Towards a Kernel based Physical Interpretation of Model Uncertainty

by   Rishabh Singh, et al.

This paper introduces a new information theoretic framework that provides a sensitive multi-modal quantification of data uncertainty by imposing a quantum physical description of its metric space. We specifically work with the kernel mean embedding metric which, apart from rendering a statistically rich data-induced representation of the signal's PDF in the RKHS, yields an intuitive physical interpretation of the signal as a potential field, resulting in its new energy based formulation. This enables one to extract multi-scale uncertainty features of data in the form of information eigenmodes by utilizing moment decomposition concepts of quantum physics. In essence, we decompose local realizations of the signal's PDF in terms of quantum uncertainty moments. Owing to its kernel basis and multi-modal nature, we postulate that such a framework would serve as a powerful surrogate tool for quantifying model uncertainty. We therefore 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.


Quantifying Model Predictive Uncertainty with Perturbation Theory

We propose a framework for predictive uncertainty quantification of a ne...

A Kernel Framework to Quantify a Model's Local Predictive Uncertainty under Data Distributional Shifts

Traditional Bayesian approaches for model uncertainty quantification rel...

Quantifying Model Uncertainty for Semantic Segmentation using Operators in the RKHS

Deep learning models for semantic segmentation are prone to poor perform...

Direct Volume Rendering with Nonparametric Models of Uncertainty

We present a nonparametric statistical framework for the quantification,...

Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive Networks

In recent years, deep learning has proven to be a viable methodology for...

Large-scale local surrogate modeling of stochastic simulation experiments

Gaussian process (GP) regression in large-data contexts, which often ari...

Uncertainty quantification for multiclass data description

In this manuscript, we propose a multiclass data description model based...