Uncertainty in Artificial Intelligence
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Metrics for Probabilistic Geometries
Alessandra Tosi, Soren Hauberg, Alfredo Vellido, Neil Lawrence
We investigate the geometrical structure of probabilistic generative dimensionality reduction models using the tools of Riemannian geometry. We explicitly define a distribution over the natu- ral 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 corre- sponding latent variable model as a Riemannian manifold and we use the expectation of the met- ric under the Gaussian process prior to define in- terpolating paths and measure distance between latent points. We show how distances that respect the expected metric lead to more appropriate gen- eration of new data.
Pages: 800-808
PS Link:
PDF Link: /papers/14/p800-tosi.pdf
AUTHOR = "Alessandra Tosi and Soren Hauberg and Alfredo Vellido and Neil Lawrence",
TITLE = "Metrics for Probabilistic Geometries",
BOOKTITLE = "Proceedings of the Thirtieth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-14)",
ADDRESS = "Corvallis, Oregon",
YEAR = "2014",
PAGES = "800--808"

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