Learning from graphs with structural variation
Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
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Learning from graphs with structural variation. / Nielsen, Rune Kok; Holm, Andreas Nugaard; Feragen, Aasa.
Neural Information Processing Systems 2017. ed. / I. Guyon; U. V. Luxburg; S. Bengio; H. Wallach; R. Fergus; S. Vishwanathan; R. Garnett. NIPS Proceedings, 2017. (Advances in Neural Information Processing Systems, Vol. 30).Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
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TY - GEN
T1 - Learning from graphs with structural variation
AU - Nielsen, Rune Kok
AU - Holm, Andreas Nugaard
AU - Feragen, Aasa
N1 - Conference code: 31
PY - 2017
Y1 - 2017
N2 - We introduce a novel framework for statistical analysis of populations of nondegenerateGaussian processes (GPs), which are natural representations of uncertaincurves. This allows inherent variation or uncertainty in function-valued data to beproperly incorporated in the population analysis. Using the 2-Wasserstein metric wegeometrize the space of GPs with L2 mean and covariance functions over compactindex spaces. We prove uniqueness of the barycenter of a population of GPs, as wellas convergence of the metric and the barycenter of their finite-dimensional counterparts.This justifies practical computations. Finally, we demonstrate our frameworkthrough experimental validation on GP datasets representing brain connectivity andclimate development. A MATLAB library for relevant computations will be publishedat https://sites.google.com/view/antonmallasto/software.
AB - We introduce a novel framework for statistical analysis of populations of nondegenerateGaussian processes (GPs), which are natural representations of uncertaincurves. This allows inherent variation or uncertainty in function-valued data to beproperly incorporated in the population analysis. Using the 2-Wasserstein metric wegeometrize the space of GPs with L2 mean and covariance functions over compactindex spaces. We prove uniqueness of the barycenter of a population of GPs, as wellas convergence of the metric and the barycenter of their finite-dimensional counterparts.This justifies practical computations. Finally, we demonstrate our frameworkthrough experimental validation on GP datasets representing brain connectivity andclimate development. A MATLAB library for relevant computations will be publishedat https://sites.google.com/view/antonmallasto/software.
M3 - Article in proceedings
T3 - Advances in Neural Information Processing Systems
BT - Neural Information Processing Systems 2017
A2 - Guyon, I.
A2 - Luxburg, U. V.
A2 - Bengio, S.
A2 - Wallach, H.
A2 - Fergus, R.
A2 - Vishwanathan, S.
A2 - Garnett, R.
PB - NIPS Proceedings
Y2 - 4 December 2017 through 9 December 2017
ER -
ID: 194814655