@inproceedings{hennig:aistats:2014,
  title = {Probabilistic Solutions to Differential Equations and their Application to Riemannian Statistics},
  booktitle = {Proceedings of the 17th International Conference on Artificial Intelligence and Statistics},
  abstract = {We study a probabilistic numerical method for the solution of both
  boundary and initial value problems that returns a joint Gaussian
  process posterior over the solution. Such methods have concrete value
  in the statistics on Riemannian manifolds, where non-analytic ordinary
  differential equations are involved in virtually all computations. The
  probabilistic formulation permits marginalising the uncertainty of the
  numerical solution such that statistics are less sensitive to
  inaccuracies. This leads to new Riemannian algorithms for mean value
  computations and principal geodesic analysis. Marginalisation also
  means results can be less precise than point estimates, enabling a
  noticeable speed-up over the state of the art. Our approach is an
  argument for a wider point that uncertainty caused by numerical
  calculations should be tracked throughout the pipeline of machine
  learning algorithms.},
  volume = {33},
  pages = {347-355},
  series = {JMLR: Workshop and Conference Proceedings},
  editors = { S Kaski and J Corander},
  publisher = {Microtome Publishing},
  address = {Brookline, MA},
  month = apr,
  year = {2014},
  author = {Hennig, Philipp and Hauberg, S{o}ren},
  month_numeric = {4}
}