Open Problem: Kernel methods on manifolds and metric spaces. What is the probability of a positive definite geodesic exponential kernel?

Aasa Feragen, Søren Hauberg. Open Problem: Kernel methods on manifolds and metric spaces. What is the probability of a positive definite geodesic exponential kernel?. In Vitaly Feldman, Alexander Rakhlin, Ohad Shamir, editors, Proceedings of the 29th Conference on Learning Theory, COLT 2016, New York, USA, June 23-26, 2016. Volume 49 of JMLR Workshop and Conference Proceedings, pages 1647-1650, JMLR.org, 2016. [doi]

@inproceedings{FeragenH16,
  title = {Open Problem: Kernel methods on manifolds and metric spaces. What is the probability of a positive definite geodesic exponential kernel?},
  author = {Aasa Feragen and Søren Hauberg},
  year = {2016},
  url = {http://jmlr.org/proceedings/papers/v49/feragen16.html},
  researchr = {https://researchr.org/publication/FeragenH16},
  cites = {0},
  citedby = {0},
  pages = {1647-1650},
  booktitle = {Proceedings of the 29th Conference on Learning Theory, COLT 2016, New York, USA, June 23-26, 2016},
  editor = {Vitaly Feldman and Alexander Rakhlin and Ohad Shamir},
  volume = {49},
  series = {JMLR Workshop and Conference Proceedings},
  publisher = {JMLR.org},
}