Nonlinear multi-output regression on unknown input manifold

Nonlinear multi-output regression on unknown input manifold Consider unknown smooth function which maps high-dimensional inputs to multidimensional outputs and whose domain of definition is unknown low-dimensional input manifold embedded in an ambient high-dimensional input space. Given training dataset consisting of ‘input-output’ pairs, regression on input manifold problem is to estimate the unknown function and its Jacobian matrix, as well to estimate the input manifold. By transforming high-dimensional inputs in their low-dimensional features, initial regression problem is reduced to certain regression on feature space problem. The paper presents a new geometrically motivated method for solving both interrelated regression problems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Mathematics and Artificial Intelligence Springer Journals

Nonlinear multi-output regression on unknown input manifold

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Publisher
Springer International Publishing
Copyright
Copyright © 2017 by Springer International Publishing Switzerland
Subject
Computer Science; Artificial Intelligence (incl. Robotics); Mathematics, general; Computer Science, general; Complex Systems
ISSN
1012-2443
eISSN
1573-7470
D.O.I.
10.1007/s10472-017-9551-0
Publisher site
See Article on Publisher Site

Abstract

Consider unknown smooth function which maps high-dimensional inputs to multidimensional outputs and whose domain of definition is unknown low-dimensional input manifold embedded in an ambient high-dimensional input space. Given training dataset consisting of ‘input-output’ pairs, regression on input manifold problem is to estimate the unknown function and its Jacobian matrix, as well to estimate the input manifold. By transforming high-dimensional inputs in their low-dimensional features, initial regression problem is reduced to certain regression on feature space problem. The paper presents a new geometrically motivated method for solving both interrelated regression problems.

Journal

Annals of Mathematics and Artificial IntelligenceSpringer Journals

Published: May 16, 2017

References

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