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Found 13 papers, 5 papers with code
Transfer Operators from Batches of Unpaired Points via Entropic Transport Kernels
In this paper, we are concerned with estimating the joint probability of random variables $X$ and $Y$, given $N$ independent observation blocks $(\boldsymbol{x}^i,\boldsymbol{y}^i)$, $i=1,\ldots, N$, each of $M$ samples $(\boldsymbol{x}^i,\boldsymbol{y}^i) = \bigl((x^i_j, y^i_{\sigma^i(j)}) \bigr)_{j=1}^M$, where $\sigma^i$ denotes an unknown permutation of i. i. d.
Manifold learning in Wasserstein space
This paper aims at building the theoretical foundations for manifold learning algorithms in the space of absolutely continuous probability measures on a compact and convex subset of $\mathbb{R}^d$, metrized with the Wasserstein-2 distance $W$.
Data-driven entropic spatially inhomogeneous evolutionary games
We prove convergence of minimizing solutions obtained from a finite number of observations to a mean field limit and the minimal value provides a quantitative error bound on the data-driven evolutions.
Optimization and Control
The Linearized Hellinger--Kantorovich Distance
Working with the local linearization and the corresponding embeddings allows for the advantages of the Euclidean setting, such as faster computations and a plethora of data analysis tools, whilst still enjoying approximately the descriptive power of the Hellinger--Kantorovich metric.
Optimization and Control
Dynamic Cell Imaging in PET with Optimal Transport Regularization
In contrast to conventional PET reconstruction our method combines the information from all detected events not only to reconstruct the dynamic evolution of the radionuclide distribution, but also to improve the reconstruction at each single time point by enforcing temporal consistency.
A Framework for Wasserstein-1-Type Metrics
We propose a unifying framework for generalising the Wasserstein-1 metric to a discrepancy measure between nonnegative measures of different mass.
Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problems
Scaling algorithms for entropic transport-type problems have become a very popular numerical method, encompassing Wasserstein barycenters, multi-marginal problems, gradient flows and unbalanced transport.
Optimization and Control Computational Engineering, Finance, and Science Numerical Analysis
Scaling Algorithms for Unbalanced Transport Problems
This article introduces a new class of fast algorithms to approximate variational problems involving unbalanced optimal transport.
Optimization and Control 65K10
Unbalanced Optimal Transport: Geometry and Kantorovich Formulation
These distances are defined by two equivalent alternative formulations: (i) a "fluid dynamic" formulation defining the distance as a geodesic distance over the space of measures (ii) a static "Kantorovich" formulation where the distance is the minimum of an optimization program over pairs of couplings describing the transfer (transport, creation and destruction) of mass between two measures.
Optimization and Control
An Interpolating Distance between Optimal Transport and Fisher-Rao
This metric interpolates between the quadratic Wasserstein and the Fisher-Rao metrics and generalizes optimal transport to measures with different masses.
Analysis of PDEs
Globally Optimal Joint Image Segmentation and Shape Matching Based on Wasserstein Modes
While the overall functional is non-convex, non-convexity is confined to a low-dimensional variable.
Contour Manifolds and Optimal Transport
Describing shapes by suitable measures in object segmentation, as proposed in [24], allows to combine the advantages of the representations as parametrized contours and indicator functions.
