Title:
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Metrics for probabilistic geometries
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Author:
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Tosi, Alessandra; Hauberg, Søren; Vellido Alcacena, Alfredo; Lawrence, Neil D.
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Ciències de la Computació; Universitat Politècnica de Catalunya. SOCO - Soft Computing |
Abstract:
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We investigate the geometrical structure of probabilistic generative dimensionality reduction models using the tools of Riemannian geometry. We explicitly define a distribution over the natural metric given by the models. We provide the necessary algorithms to compute expected metric tensors where the distribution over mappings is
given by a Gaussian process. We treat the corresponding latent variable model as a Riemannian manifold and we use the expectation of the metric under the Gaussian process prior to define interpolating paths and measure distance between latent points. We show how distances that respect the expected metric lead to more appropriate generation of new data. |
Abstract:
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Peer Reviewed |
Subject(s):
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-Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica -Geometry, Riemannian -Gaussian processes -Riemann, Geometria de -Processos gaussians |
Rights:
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Document type:
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Article - Submitted version Conference Object |
Published by:
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AUAI Press (Association for Uncertainty in Artificial Intelligence)
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