A Physics inspired Functional Operator for Model Uncertainty Quantification in the RKHS
This work addresses the need for efficient and accurate uncertainty quantification in ML models, particularly for applications sensitive to prediction reliability, though it appears incremental as it builds on existing RKHS and physics concepts.
The authors tackled the problem of expensive and inaccurate uncertainty quantification in machine learning by proposing a fast single-shot framework using physics-inspired functional operators in RKHS, which achieved more precise and better calibrated uncertainty estimates than baseline methods on covariate shifted test data.
Accurate uncertainty quantification of model predictions is a crucial problem in machine learning. Existing Bayesian methods, being highly iterative, are expensive to implement and often fail to accurately capture a model's true posterior because of their tendency to select only central moments. We propose a fast single-shot uncertainty quantification framework where, instead of working with the conventional Bayesian definition of model weight probability density function (PDF), we utilize physics inspired functional operators over the projection of model weights in a reproducing kernel Hilbert space (RKHS) to quantify their uncertainty at each model output. The RKHS projection of model weights yields a potential field based interpretation of model weight PDF which consequently allows the definition of a functional operator, inspired by perturbation theory in physics, that performs a moment decomposition of the model weight PDF (the potential field) at a specific model output to quantify its uncertainty. We call this representation of the model weight PDF as the quantum information potential field (QIPF) of the weights. The extracted moments from this approach automatically decompose the weight PDF in the local neighborhood of the specified model output and determine, with great sensitivity, the local heterogeneity of the weight PDF around a given prediction. These moments therefore provide sharper estimates of predictive uncertainty than central stochastic moments of Bayesian methods. Experiments evaluating the error detection capability of different uncertainty quantification methods on covariate shifted test data show our approach to be more precise and better calibrated than baseline methods, while being faster to compute.