Distribution-Free Uncertainty Quantification for Kernel Methods by Gradient Perturbations

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.Comment: 18 figure

Production trend identification and forecast for shop-floor business intelligence

The paper introduces a methodology to define production trend classes and also the results to serve with trend prognosis in a given manufacturing situation. The prognosis is valid for one, selected production measure (e.g. a quality dimension of one product, like diameters, angles, surface roughness, pressure, basis position, etc.) but the applied model takes into account the past values of many other, related production data collected typically on the shop-floor, too. Consequently, it is useful in batch or (customized) mass production environments. The proposed solution is applicable to realize production control inside the tolerance limits to proactively avoid the production process going outside from the given upper and lower tolerance limits. The solution was developed and validated on real data collected on the shop-floor; the paper also summarizes the validated application results of the proposed methodology. © 2016, IMEKO-International Measurement Federation Secretariat. All rights reserved