442 citations · 2.5k across the 75 of their papers we have counts for
6 papers · 1 filter
Log-PCA versus Geodesic PCA of histograms in the Wasserstein space
Elsa Cazelles, Vivien Seguy, Jérémie Bigot +2
This paper is concerned by the statistical analysis of data sets whose elements are random histograms. For the purpose of learning principal modes of variation from such data, we c…
Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learning
Morgan A. Schmitz, Matthieu Heitz, Nicolas Bonneel +5
This paper introduces a new nonlinear dictionary learning method for histograms in the probability simplex. The method leverages optimal transport theory, in the sense that our aim…
GAN and VAE from an Optimal Transport Point of View
Aude Genevay, Gabriel Peyré, Marco Cuturi
This short article revisits some of the ideas introduced in arXiv:1701.07875 and arXiv:1705.07642 in a simple setup. This sheds some lights on the connexions between Variational Au…
Sliced Wasserstein Kernel for Persistence Diagrams
Mathieu Carrière, Marco Cuturi, Steve Oudot
Persistence diagrams (PDs) play a key role in topological data analysis (TDA), in which they are routinely used to describe topological properties of complicated shapes. PDs enjoy…
Learning Generative Models with Sinkhorn Divergences
Aude Genevay, Gabriel Peyré, Marco Cuturi
The ability to compare two degenerate probability distributions (i.e. two probability distributions supported on two distinct low-dimensional manifolds living in a much higher-dime…
Soft-DTW: a Differentiable Loss Function for Time-Series
Marco Cuturi, Mathieu Blondel
We propose in this paper a differentiable learning loss between time series, building upon the celebrated dynamic time warping (DTW) discrepancy. Unlike the Euclidean distance, DTW…