Metrics for Probabilistic Geometries

Alessandra Tosi, Søren Hauberg, Alfredo Vellido, Neil D. Lawrence

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Abstract

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.
Original languageEnglish
Title of host publicationProceedings of 30th Conference on Uncertainty in Artificial Intelligence (UAI 2014)
EditorsNevin L. Zhang, Jin Tian
PublisherAUAI Press Corvallis
Publication date2014
Pages800-809
ISBN (Electronic)978-0-9749039-1-0
Publication statusPublished - 2014
Event30th Conference on Uncertainty in Artificial Intelligence (UAI 2014) - Quebec City, Canada
Duration: 23 Jul 201427 Jul 2014
Conference number: 20
http://auai.org/uai2014/

Conference

Conference30th Conference on Uncertainty in Artificial Intelligence (UAI 2014)
Number20
CountryCanada
CityQuebec City
Period23/07/201427/07/2014
Internet address

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