Metrics for Probabilistic Geometries
Machine Learning
2014-12-01 v1 Machine Learning
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.
Cite
@article{arxiv.1411.7432,
title = {Metrics for Probabilistic Geometries},
author = {Alessandra Tosi and Søren Hauberg and Alfredo Vellido and Neil D. Lawrence},
journal= {arXiv preprint arXiv:1411.7432},
year = {2014}
}
Comments
UAI 2014