arXiv Analytics

Sign in

arXiv:1812.09632 [cs.LG]AbstractReferencesReviewsResources

Uncertainty Quantification for Kernel Methods

Balázs Csanád Csáji, Krisztián Balázs Kis

Published 2018-12-23Version 1

We propose a data-driven approach to quantify the uncertainty of models constructed by kernel methods. Our approach minimizes the needed distributional assumptions, hence, instead of working with, for example, Gaussian processes or exponential families, it only requires knowledge about some mild regularity of the measurement noise, such as it is being symmetric or exchangeable. We show, by building on recent results from finite-sample system identification, that by perturbing the residuals in the gradient of the objective function, information can be extracted about the amount of uncertainty our model has. Particularly, we provide an algorithm to build exact, non-asymptotically guaranteed, distribution-free confidence regions for ideal, noise-free representations of the function we try to estimate. For the typical convex quadratic problems and symmetric noises, the regions are star convex centered around a given nominal estimate, and have efficient ellipsoidal outer approximations. Finally, we illustrate the ideas on typical kernel methods, such as LS-SVC, KRR, kernelized LASSO and $\varepsilon$-SVR.

Related articles: Most relevant | Search more
arXiv:2302.04019 [cs.LG] (Published 2023-02-08)
Fortuna: A Library for Uncertainty Quantification in Deep Learning
arXiv:2302.04730 [cs.LG] (Published 2023-02-09)
A Benchmark on Uncertainty Quantification for Deep Learning Prognostics
arXiv:2306.14430 [cs.LG] (Published 2023-06-26)
Enhanced multi-fidelity modelling for digital twin and uncertainty quantification