Aggregating Algorithm competing with Banach lattices
Machine Learning
2010-02-04 v1
Abstract
The paper deals with on-line regression settings with signals belonging to a Banach lattice. Our algorithms work in a semi-online setting where all the inputs are known in advance and outcomes are unknown and given step by step. We apply the Aggregating Algorithm to construct a prediction method whose cumulative loss over all the input vectors is comparable with the cumulative loss of any linear functional on the Banach lattice. As a by-product we get an algorithm that takes signals from an arbitrary domain. Its cumulative loss is comparable with the cumulative loss of any predictor function from Besov and Triebel-Lizorkin spaces. We describe several applications of our setting.
Cite
@article{arxiv.1002.0709,
title = {Aggregating Algorithm competing with Banach lattices},
author = {Fedor Zhdanov and Alexey Chernov and Yuri Kalnishkan},
journal= {arXiv preprint arXiv:1002.0709},
year = {2010}
}