PublisherAUAI Press (Association for Uncertainty in Artificial Intelligence)
Rights accessRestricted access - publisher's policy
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.
CitationTosi, A., Hauberg, S., Vellido, A., Lawrence, N. Metrics for probabilistic geometries. A: Conference on Uncertainty in Artificial Intelligence. "Uncertainty in Artificial Intelligence: proceedings of the thirtieth conference (2014): July 23-27, 2014, Quebec City, Quebec, Canada". Quebec: AUAI Press (Association for Uncertainty in Artificial Intelligence), 2014, p. 800-808.
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