Self-normalization techniques for streaming confident regression

摘要: We consider, in a generic streaming regression setting, the problem of building confidence interval (and distribution) on next observation based past observed data. The observations given to learner are form (x, y) with y = f (x) + ξ, where x can have arbitrary dependency observations, is unknown and noise ξ sub-Gaussian conditionally observations. Further, assumed come from some external filtering process making number itself random stopping time. In this challenging scenario that captures large class processes non-anticipative dependencies, we study ordinary, ridge, kernel least-squares estimates provide intervals self-normalized vector-valued martingale techniques, applied estimation mean variance. then discuss how these adaptive be used order detect possible model mismatch as well estimate future (self-information, quadratic, or transportation) loss at step.