Browsing by Subject "Nonlinear adaptive filtering"

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Open Access
A comprehensive approach to universal piecewise nonlinear regression based on trees
(IEEE, 2014) Vanli, N. D.; Kozat, S. S.
In this paper, we investigate adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an individual sequence manner. We use a tree notion in order to partition the space of regressors in a nested structure. The introduced algorithms adapt not only their regression functions but also the complete tree structure while achieving the performance of the 'best' linear mixture of a doubly exponential number of partitions, with a computational complexity only polynomial in the number of nodes of the tree. While constructing these algorithms, we also avoid using any artificial 'weighting' of models (with highly data dependent parameters) and, instead, directly minimize the final regression error, which is the ultimate performance goal. The introduced methods are generic such that they can readily incorporate different tree construction methods such as random trees in their framework and can use different regressor or partitioning functions as demonstrated in the paper.
Open Access
Piecewise nonlinear regression via decision adaptive trees
(IEEE, 2014-09) Vanlı, N. Denizcan; Sayın, Muhammed O.; Ergüt, S.; Kozat, Süleyman S.
We investigate the problem of adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an individual sequence manner. We partition the regressor space using hyperplanes in a nested structure according to the notion of a tree. In this manner, we introduce an adaptive nonlinear regression algorithm that not only adapts the regressor of each partition but also learns the complete tree structure with a computational complexity only polynomial in the number of nodes of the tree. Our algorithm is constructed to directly minimize the final regression error without introducing any ad-hoc parameters. Moreover, our method can be readily incorporated with any tree construction method as demonstrated in the paper. © 2014 EURASIP.