3 accepted papers
Cech Persistence diagrams (PDs) are topological descriptors routinely used to capture the geometry of complex datasets. They are commonly compared using the Wasserstein distances $\mathrm{OT}_p$; however, the extent to which PDs are stable with respect to these metrics remains poorly understood. We…
We consider the problem of estimating the optimal transport map between two probability distributions, $P$ and $Q$ in $\mathbb{R}^d$, on the basis of i.i.d. samples. All existing statistical analyses of this problem require the assumption that the transport map is Lipschitz, a strong requirement tha…
Persistence diagrams (PDs) are the most common descriptors used to encode the topology of structured data appearing in challenging learning tasks; think e.g. of graphs, time series or point clouds sampled close to a manifold. Given random objects and the corresponding distribution of PDs, one may wa…