• Corpus ID: 15177472

Metrics for Probabilistic Geometries

  title={Metrics for Probabilistic Geometries},
  author={Alessandra Tosi and S{\o}ren Hauberg and Alfredo Vellido and Neil D. 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 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… 

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  • D. RamananS. Baker
  • Computer Science
    IEEE Transactions on Pattern Analysis and Machine Intelligence
  • 2011
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