70 Citations
Measure Estimation in the Barycentric Coding Model
- Computer Science, MathematicsICML
- 2022
This paper provides novel geometrical, statistical, and computational insights for measure estimation under the barycentric coding model (BCM), and establishes an algorithm for solving for the coordinates in the BCM when all the measures are observed empirically via i.i.d. samples.
Projected Statistical Methods for Distributional Data on the Real Line with the Wasserstein Metric
- Computer ScienceJ. Mach. Learn. Res.
- 2022
We present a novel class of projected methods, to perform statistical analysis on a data set of probability distributions on the real line, with the 2-Wasserstein metric. We focus in particular on…
Fast PCA in 1-D Wasserstein Spaces via B-splines Representation and Metric Projection
- Computer ScienceAAAI
- 2021
A novel definition of Principal Component Analysis in the Wasserstein space is proposed that yields a straightforward optimization problem that is extremely fast to compute and performs similarly to the ones already proposed in the literature while retaining a much smaller computational cost.
Graphical and uniform consistency of estimated optimal transport plans
- Mathematics
- 2022
A general theory is provided delivering convergence of maximal cyclically monotone mappings containing the supports of coupling measures of sequences of pairs of possibly random probability measures…
Wasserstein multivariate auto-regressive models for modeling distributional time series and its application in graph learning
- Mathematics, Computer ScienceArXiv
- 2022
A new auto-regressive model for the statistical analysis of multivariate distributional time series using the theory of iterated random function systems and a consistent estimator for the model coefficient is proposed.
Nonlinear Sufficient Dimension Reduction for Distribution-on-Distribution Regression
- Computer Science
- 2022
A novel framework for nonlinear sufficient dimension reduction where both the predictor and the response are distributional data, which are modeled as members of a metric space to build universal kernels on the metric spaces.
Measuring dependence between random vectors via optimal transport
- MathematicsJ. Multivar. Anal.
- 2022
On some connections between Esscher's tilting, saddlepoint approximations, and optimal transportation: a statistical perspective
- Mathematics
- 2021
We showcase some unexplored connections between saddlepoint approximations, measure transportation, and some key topics in information theory. To bridge these different areas, we review selectively…
Kantorovich-Rubinstein distance and barycenter for finitely supported measures: Foundations and Algorithms
- Computer Science, Mathematics
- 2021
A systematic discussion of a generalized barycenter based on a variant of unbalanced optimal transport (UOT) that allows for mass creation and destruction modeled by some cost parameter and its structure to be explicitly specified by the support of the input measures.
Multiple Oracle Algorithm For General-Sum Continuous Games
- Computer ScienceArXiv
- 2021
This contribution proposes an iterative strategy generation technique, which splits the original problem into the master problem with only a finite subset of strategies being considered, and the subproblem in which an oracle finds the best response of each player, and convergence in the Wasserstein distance to an equilibrium of the original continuous game.
References
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A key element in this approach is to demonstrate that when the classical phase variation assumptions of Functional Data Analysis are applied to the point process case, they become equivalent to conditions interpretable through the prism of the theory of optimal transportation of measure.
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Barycenters in the Wasserstein Space
- Mathematics, Computer ScienceSIAM J. Math. Anal.
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