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Found 19 papers, 12 papers with code
Semi-Discrete Optimal Transport: Nearly Minimax Estimation With Stochastic Gradient Descent and Adaptive Entropic Regularization
In this work, we answer positively to this question by (i) proving an $\mathcal{O}(t^{-1})$ lower bound rate for the OT map, using the similarity between Laguerre cells estimation and density support estimation, and (ii) proposing a Stochastic Gradient Descent (SGD) algorithm with adaptive entropic regularization and averaging acceleration.
Understanding the training of infinitely deep and wide ResNets with Conditional Optimal Transport
We study the convergence of gradient flow for the training of deep neural networks.
GradICON: Approximate Diffeomorphisms via Gradient Inverse Consistency
We present an approach to learning regular spatial transformations between image pairs in the context of medical image registration.
Unbalanced Optimal Transport, from Theory to Numerics
Optimal Transport (OT) has recently emerged as a central tool in data sciences to compare in a geometrically faithful way point clouds and more generally probability distributions.
$\texttt{GradICON}$: Approximate Diffeomorphisms via Gradient Inverse Consistency
We present an approach to learning regular spatial transformations between image pairs in the context of medical image registration.
Toric Geometry of Entropic Regularization
Entropic regularization is a method for large-scale linear programming.
Faster Unbalanced Optimal Transport: Translation invariant Sinkhorn and 1-D Frank-Wolfe
In this work, we identify the cause for this deficiency, namely the lack of a global normalization of the iterates, which equivalently corresponds to a translation of the dual OT potentials.
Global convergence of ResNets: From finite to infinite width using linear parameterization
To bridge the gap between the lazy and mean field regimes, we study Residual Networks (ResNets) in which the residual block has linear parametrization while still being nonlinear.
Near-optimal estimation of smooth transport maps with kernel sums-of-squares
It was recently shown that under smoothness conditions, the squared Wasserstein distance between two distributions could be efficiently computed with appealing statistical error upper bounds.
The Unbalanced Gromov Wasserstein Distance: Conic Formulation and Relaxation
The GW distance is however limited to the comparison of metric measure spaces endowed with a probability distribution.
A Shooting Formulation of Deep Learning
Continuous-depth neural networks can be viewed as deep limits of discrete neural networks whose dynamics resemble a discretization of an ordinary differential equation (ODE).
Faster Wasserstein Distance Estimation with the Sinkhorn Divergence
We also propose and analyze an estimator based on Richardson extrapolation of the Sinkhorn divergence which enjoys improved statistical and computational efficiency guarantees, under a condition on the regularity of the approximation error, which is in particular satisfied for Gaussian densities.
Sinkhorn Divergences for Unbalanced Optimal Transport
Optimal transport induces the Earth Mover's (Wasserstein) distance between probability distributions, a geometric divergence that is relevant to a wide range of problems.
Region-specific Diffeomorphic Metric Mapping
We introduce a region-specific diffeomorphic metric mapping (RDMM) registration approach.
Ranked #1 on
Image Registration
on Osteoarthritis Initiative
Interpolating between Optimal Transport and MMD using Sinkhorn Divergences
Comparing probability distributions is a fundamental problem in data sciences.
Statistics Theory Statistics Theory 62
Quantum Optimal Transport for Tensor Field Processing
This "quantum" formulation of OT (Q-OT) corresponds to a relaxed version of the classical Kantorovich transport problem, where the fidelity between the input PSD-valued measures is captured using the geometry of the Von-Neumann quantum entropy.
Graphics
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
