Infinitesimal behavior of quadratically regularized optimal transport and its relation with the porous medium equation
A Garriz-Molina, A González-Sanz… - arxiv preprint arxiv …, 2024 - arxiv.org
The quadratically regularized optimal transport problem has recently been considered in
various applications where the coupling needs to be\emph {sparse}, ie, the density of the …
various applications where the coupling needs to be\emph {sparse}, ie, the density of the …
Sparsity of quadratically regularized optimal transport: Scalar case
The quadratically regularized optimal transport problem is empirically known to have sparse
solutions: its optimal coupling $\pi_ {\varepsilon} $ has sparse support for small …
solutions: its optimal coupling $\pi_ {\varepsilon} $ has sparse support for small …
Quantitative convergence of quadratically regularized linear programs
Linear programs with quadratic regularization are attracting renewed interest due to their
applications in optimal transport: unlike entropic regularization, the squared-norm penalty …
applications in optimal transport: unlike entropic regularization, the squared-norm penalty …
Nonlinear inverse optimal transport: Identifiability of the transport cost from its marginals and optimal values
The inverse optimal transport problem is to find the underlying cost function from the
knowledge of optimal transport plans. While this amounts to solving a linear inverse …
knowledge of optimal transport plans. While this amounts to solving a linear inverse …
Monotonicity in quadratically regularized linear programs
In optimal transport, quadratic regularization is a sparse alternative to entropic
regularization: the solution measure tends to have small support. Computational experience …
regularization: the solution measure tends to have small support. Computational experience …
Sparsity of quadratically regularized optimal transport: Bounds on concentration and bias
We study the quadratically regularized optimal transport (QOT) problem for quadratic cost
and compactly supported marginals $\mu $ and $\nu $. It has been empirically observed that …
and compactly supported marginals $\mu $ and $\nu $. It has been empirically observed that …
Entropic Optimal Transport Eigenmaps for Nonlinear Alignment and Joint Embedding of High-Dimensional Datasets
Embedding high-dimensional data into a low-dimensional space is an indispensable
component of data analysis. In numerous applications, it is necessary to align and jointly …
component of data analysis. In numerous applications, it is necessary to align and jointly …
The entropic optimal (self-) transport problem: Limit distributions for decreasing regularization with application to score function estimation
G Mordant - arxiv preprint arxiv:2412.12007, 2024 - arxiv.org
Westudythestatisticalpropertiesoftheentropi… (self) transport problem for smooth probability
measures. We provide an accurate description of the limit distribution for entropic (self-) …
measures. We provide an accurate description of the limit distribution for entropic (self-) …
Regularised optimal self-transport is approximate Gaussian mixture maximum likelihood
G Mordant - International Conference on Soft Methods in Probability …, 2024 - Springer
We investigate the link between regularised self-transport problems and maximum
likelihood estimation in Gaussian mixture models (GMM). This link suggests that self …
likelihood estimation in Gaussian mixture models (GMM). This link suggests that self …
Quadratically Regularized Optimal Transport: Existence and Multiplicity of Potentials
M Nutz - arxiv preprint arxiv:2404.06847, 2024 - arxiv.org
The optimal transport problem with quadratic regularization is useful when sparse couplings
are desired. The density of the optimal coupling is described by two functions called …
are desired. The density of the optimal coupling is described by two functions called …