Computational optimal transport: With applications to data science
Optimal transport (OT) theory can be informally described using the words of the French
mathematician Gaspard Monge (1746–1818): A worker with a shovel in hand has to move a …
mathematician Gaspard Monge (1746–1818): A worker with a shovel in hand has to move a …
Recent advances in optimal transport for machine learning
EF Montesuma, FMN Mboula… - IEEE Transactions on …, 2024 - ieeexplore.ieee.org
Recently, Optimal Transport has been proposed as a probabilistic framework in Machine
Learning for comparing and manipulating probability distributions. This is rooted in its rich …
Learning for comparing and manipulating probability distributions. This is rooted in its rich …
Unbalanced minibatch optimal transport; applications to domain adaptation
Optimal transport distances have found many applications in machine learning for their
capacity to compare non-parametric probability distributions. Yet their algorithmic complexity …
capacity to compare non-parametric probability distributions. Yet their algorithmic complexity …
Supervised training of conditional monge maps
Optimal transport (OT) theory describes general principles to define and select, among many
possible choices, the most efficient way to map a probability measure onto another. That …
possible choices, the most efficient way to map a probability measure onto another. That …
Geometric dataset distances via optimal transport
D Alvarez-Melis, N Fusi - Advances in Neural Information …, 2020 - proceedings.neurips.cc
The notion of task similarity is at the core of various machine learning paradigms, such as
domain adaptation and meta-learning. Current methods to quantify it are often heuristic …
domain adaptation and meta-learning. Current methods to quantify it are often heuristic …
Faster Wasserstein distance estimation with the Sinkhorn divergence
The squared Wasserstein distance is a natural quantity to compare probability distributions
in a non-parametric setting. This quantity is usually estimated with the plug-in estimator …
in a non-parametric setting. This quantity is usually estimated with the plug-in estimator …
Conditional sig-wasserstein gans for time series generation
Generative adversarial networks (GANs) have been extremely successful in generating
samples, from seemingly high dimensional probability measures. However, these methods …
samples, from seemingly high dimensional probability measures. However, these methods …
Statistical bounds for entropic optimal transport: sample complexity and the central limit theorem
G Mena, J Niles-Weed - Advances in neural information …, 2019 - proceedings.neurips.cc
We prove several fundamental statistical bounds for entropic OT with the squared Euclidean
cost between subgaussian probability measures in arbitrary dimension. First, through a new …
cost between subgaussian probability measures in arbitrary dimension. First, through a new …
Entropic estimation of optimal transport maps
AA Pooladian, J Niles-Weed - arXiv preprint arXiv:2109.12004, 2021 - arxiv.org
We develop a computationally tractable method for estimating the optimal map between two
distributions over $\mathbb {R}^ d $ with rigorous finite-sample guarantees. Leveraging an …
distributions over $\mathbb {R}^ d $ with rigorous finite-sample guarantees. Leveraging an …
The monge gap: A regularizer to learn all transport maps
Optimal transport (OT) theory has been used in machine learning to study and characterize
maps that can push-forward efficiently a probability measure onto another. Recent works …
maps that can push-forward efficiently a probability measure onto another. Recent works …