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Found 27 papers, 4 papers with code
Supervised Quantile Normalization for Low Rank Matrix Factorization
Low rank matrix factorization is a fundamental building block in machine learning, used for instance to summarize gene expression profile data or word-document counts.
Trajectory Inference with Smooth Schrödinger Bridges
Motivated by applications in trajectory inference and particle tracking, we introduce Smooth Schr\"odinger Bridges.
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.
Learning large softmax mixtures with warm start EM
We develop a new MoM parameter estimator based on latent moment estimation that is tailored to our model, and provide the first theoretical analysis for a MoM-based procedure in softmax mixtures.
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.
Convergence of Unadjusted Langevin in High Dimensions: Delocalization of Bias
The unadjusted Langevin algorithm is commonly used to sample probability distributions in extremely high-dimensional settings.
Statistical optimal transport
We present an introduction to the field of statistical optimal transport, based on lectures given at \'Ecole d'\'Et\'e de Probabilit\'es de Saint-Flour XLIX.
Progressive Entropic Optimal Transport Solvers
Optimal transport (OT) has profoundly impacted machine learning by providing theoretical and computational tools to realign datasets.
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.
The Adversarial Consistency of Surrogate Risks for Binary Classification
We study the consistency of surrogate risks for robust binary classification.
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}.
Perturbation Analysis of Neural Collapse
In this paper, we propose a richer model that can capture this phenomenon by forcing the features to stay in the vicinity of a predefined features matrix (e. g., intermediate features).
Estimation and inference for the Wasserstein distance between mixing measures in topic models
Our results establish this metric to be a canonical choice.
The Consistency of Adversarial Training for Binary Classification
Robustness to adversarial perturbations is of paramount concern in modern machine learning.
Existence and Minimax Theorems for Adversarial Surrogate Risks in Binary Classification
Adversarial training is one of the most popular methods for training methods robust to adversarial attacks, however, it is not well-understood from a theoretical perspective.
An improved central limit theorem and fast convergence rates for entropic transportation costs
We prove a central limit theorem for the entropic transportation cost between subgaussian probability measures, centered at the population cost.
Deep Probability Estimation
Reliable probability estimation is of crucial importance in many real-world applications where there is inherent (aleatoric) uncertainty.
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.
Plugin Estimation of Smooth Optimal Transport Maps
Our work also provides new bounds on the risk of corresponding plugin estimators for the quadratic Wasserstein distance, and we show how this problem relates to that of estimating optimal transport maps using stability arguments for smooth and strongly convex Brenier potentials.
It was "all" for "nothing": sharp phase transitions for noiseless discrete channels
We establish a phase transition known as the "all-or-nothing" phenomenon for noiseless discrete channels.
Statistics Theory Information Theory Information Theory Probability Statistics Theory
Streaming k-PCA: Efficient guarantees for Oja's algorithm, beyond rank-one updates
We analyze Oja's algorithm for streaming $k$-PCA and prove that it achieves performance nearly matching that of an optimal offline algorithm.
The Discrepancy of Random Rectangular Matrices
A recent approach to the Beck-Fiala conjecture, a fundamental problem in combinatorics, has been to understand when random integer matrices have constant discrepancy.
Probability Discrete Mathematics Combinatorics
Sinkhorn EM: An Expectation-Maximization algorithm based on entropic optimal transport
We study Sinkhorn EM (sEM), a variant of the expectation maximization (EM) algorithm for mixtures based on entropic optimal transport.
Early-Learning Regularization Prevents Memorization of Noisy Labels
In contrast with existing approaches, which use the model output during early learning to detect the examples with clean labels, and either ignore or attempt to correct the false labels, we take a different route and instead capitalize on early learning via regularization.
Ranked #5 on
Learning with noisy labels
on CIFAR-10N-Random2
Supervised Quantile Normalization for Low-rank Matrix Approximation
Low rank matrix factorization is a fundamental building block in machine learning, used for instance to summarize gene expression profile data or word-document counts.
Massively scalable Sinkhorn distances via the Nyström method
The Sinkhorn "distance", a variant of the Wasserstein distance with entropic regularization, is an increasingly popular tool in machine learning and statistical inference.
