Self-normalization techniques for streaming confident regression

Odalric-Ambrym Maillard 1, *
* Auteur correspondant
1 TAO - Machine Learning and Optimisation
LRI - Laboratoire de Recherche en Informatique, UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR8623
Abstract : We consider, in a generic streaming regression setting, the problem of building a confidence interval (and distribution) on the next observation based on past observed data. The observations given to the learner are of the form (x, y) with y = f (x) + ξ, where x can have arbitrary dependency on the past observations, f is unknown and the noise ξ is sub-Gaussian conditionally on the past observations. Further, the observations are assumed to come from some external filtering process making the number of observations itself a random stopping time. In this challenging scenario that captures a large class of processes with non-anticipative dependencies, we study the ordinary, ridge, and kernel least-squares estimates and provide confidence intervals based on self-normalized vector-valued martingale techniques, applied to the estimation of the mean and of the variance. We then discuss how these adaptive confidence intervals can be used in order to detect a possible model mismatch as well as to estimate the future (self-information, quadratic, or transportation) loss of the learner at a next step.
Type de document :
Pré-publication, Document de travail
2016
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https://hal.archives-ouvertes.fr/hal-01349727
Contributeur : Odalric-Ambrym Maillard <>
Soumis le : vendredi 29 juillet 2016 - 10:07:36
Dernière modification le : vendredi 10 mars 2017 - 01:09:03
Document(s) archivé(s) le : dimanche 30 octobre 2016 - 12:04:38

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  • HAL Id : hal-01349727, version 1

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Odalric-Ambrym Maillard. Self-normalization techniques for streaming confident regression. 2016. 〈hal-01349727v1〉

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