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Found 15 papers, 6 papers with code
Conditional simulation via entropic optimal transport: Toward non-parametric estimation of conditional Brenier maps
Conditional simulation is a fundamental task in statistical modeling: Generate samples from the conditionals given finitely many data points from a joint distribution.
Plug-in estimation of Schrödinger bridges
Instead, we show that the potentials obtained from solving the static entropic optimal transport problem between the source and target samples can be modified to yield a natural plug-in estimator of the time-dependent drift that defines the bridge between two measures.
Progressive Entropic Optimal Transport Solvers
Optimal transport (OT) has profoundly impacted machine learning by providing theoretical and computational tools to realign datasets.
Neural Optimal Transport with Lagrangian Costs
We investigate the optimal transport problem between probability measures when the underlying cost function is understood to satisfy a least action principle, also known as a Lagrangian cost.
Algorithms for mean-field variational inference via polyhedral optimization in the Wasserstein space
We develop a theory of finite-dimensional polyhedral subsets over the Wasserstein space and optimization of functionals over them via first-order methods.
Learning Elastic Costs to Shape Monge Displacements
Given a source and a target probability measure supported on $\mathbb{R}^d$, the Monge problem asks to find the most efficient way to map one distribution to the other.
Multisample Flow Matching: Straightening Flows with Minibatch Couplings
Simulation-free methods for training continuous-time generative models construct probability paths that go between noise distributions and individual data samples.
An Explicit Expansion of the Kullback-Leibler Divergence along its Fisher-Rao Gradient Flow
In this short note, we complement these existing results in the literature by providing an explicit expansion of $\text{KL}(\rho_t^{\text{FR}}\|\pi)$ in terms of $e^{-t}$, where $(\rho_t^{\text{FR}})_{t\geq 0}$ is the FR gradient flow of the KL divergence.
Minimax estimation of discontinuous optimal transport maps: The semi-discrete case
We consider the problem of estimating the optimal transport map between two probability distributions, $P$ and $Q$ in $\mathbb R^d$, on the basis of i. i. d.
Optimal transport map estimation in general function spaces
To ensure identifiability, we assume that $T = \nabla \varphi_0$ is the gradient of a convex function, in which case $T$ is known as an \emph{optimal transport map}.
Entropic estimation of optimal transport maps
We develop a computationally tractable method for estimating the optimal map between two distributions over $\mathbb{R}^d$ with rigorous finite-sample guarantees.
Learning normalizing flows from Entropy-Kantorovich potentials
We approach the problem of learning continuous normalizing flows from a dual perspective motivated by entropy-regularized optimal transport, in which continuous normalizing flows are cast as gradients of scalar potential functions.
Farkas layers: don't shift the data, fix the geometry
Successfully training deep neural networks often requires either batch normalization, appropriate weight initialization, both of which come with their own challenges.
A principled approach for generating adversarial images under non-smooth dissimilarity metrics
This includes, but is not limited to, $\ell_1, \ell_2$, and $\ell_\infty$ perturbations; the $\ell_0$ counting "norm" (i. e. true sparseness); and the total variation seminorm, which is a (non-$\ell_p$) convolutional dissimilarity measuring local pixel changes.
The LogBarrier adversarial attack: making effective use of decision boundary information
Adversarial attacks formally correspond to an optimization problem: find a minimum norm image perturbation, constrained to cause misclassification.
