Neural Information Processing Systems http://nips.cc/

We reveal which problems in unbalanced optimal transport can/cannot be solved efficiently.

More generally, any finite subset of a hyperbolic space "looks like" a finite tree.

Because cardinality is a simple property of any set, we argue that such bounds do not fully capture the rich structure endowed by the metric.

More generally, any finite subset of a hyperbolic space "looks like" a finite tree.

Neural Information Processing Systems http://nips.cc/

Although Prop. 2 follows from Prop. 1, it follows the idea An upper bound on the Euclidean OT[...] The We will insist more on the importance of sampling tree metrics randomly, both for low-dimensional in 6.1 Definite-negativity is mentioned and highlighted[...] explain why is it important Is this to ensure that the kernel is positive-definite? This is why kernel methods kick in from .6 (or Gaussian processes as per Reviewer #2's suggestion). Indeed, averaging of negative definite functions is trivially negative definite. We used the farthest-point clustering due to its fast computation, i.e.

We reveal which problems in unbalanced optimal transport can/cannot be solved efficiently.