aiqbench analysis
This paper introduces a distribution-free method for quantifying uncertainty in kernel-based machine learning models by perturbing gradient residuals, eliminating the need for strict assumptions like Gaussian noise. By providing exact, non-asymptotic confidence regions for various kernel methods such as KRR and LS-SVC, it offers a robust framework for assessing model reliability without relying on exponential families.
Distribution-Free Uncertainty Quantification for Kernel Methods by Gradient Perturbations
arXiv:1812.09632v3 Announce Type: replace Abstract: 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, $\varepsilon$-SVR and kernelized LASSO.
Abstract: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, $\varepsilon$-SVR and kernelized LASSO.
Machine Learning (cs.LG); Machine Learning (stat.ML)
arXiv:1812.09632 [cs.LG]
(or arXiv:1812.09632v3 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.1812.09632 Focus to learn more arXiv-issued DOI via DataCite
Machine Learning, Volume 108, Issue 8, 2019, pp. 1677-1699
https://doi.org/10.1007/s10994-019-05822-1 Focus to learn more DOI(s) linking to related resources
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