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Statistical optimal transport
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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.
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Cited by 13 Pith papers
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The Score Hamiltonian: Mapping Diffusion Models to Adiabatic Transport
Score-based diffusion sampling is shown to be adiabatic ground-state transport for a Score Hamiltonian, with error floor equal to terminal score-matching error over the square root of the spectral gap.
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Optimizing the Preconditioner: A Black-box Online-to-Nonconvex Conversion with Static Regret Minimization Oracles
An OCO algorithm with only O(√T) static regret, pluggable as a preconditioner selector, recovers the classical O(1/√T) stationarity rate on smooth stochastic nonconvex problems and the O(T^{-2/7}) rate on nonsmooth ones.
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Convergence Rates for Distribution Matching with Sliced Optimal Transport
For Gaussian distributions, slice-matching to an isotropic target with decaying step sizes converges at rate O(k^{-(2α-1)}) in expectation.
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Convergence of drift-diffusion PDEs arising as Wasserstein gradient flows of convex functions
Wasserstein gradient flows of linearly convex objectives with an entropy term converge at explicit rates: O(1/t) under plain convexity, and arbitrarily fast polynomial or exponential rates under entropy-strong convexity.
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PCA of probability measures: Sparse and Dense sampling regimes
PCA of random probability measures converges at rate n^{-1/2}+m^{-α} in the double asymptotic regime, with the dense-regime covariance rate minimax optimal.
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Robust Simulation Based Inference
A robust SBI framework that provides valid frequentist inference under model misspecification by targeting projection parameters and expanding models through exponential tilting.
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Fast Convergence for High-Order ODE Solvers in Diffusion Probabilistic Models
A TV convergence bound O(d^{7/4} ε^{1/2} + d(dH)^p) is proved for p-th order (exponential) Runge-Kutta samplers of probability-flow ODEs under C² smoothness of the learned score.
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Optimal Transport with Heterogeneously Missing Data
A debiased Bures-Wasserstein estimator and a matrix-completion based estimator for entropic optimal transport are consistent under heterogeneous MCAR missingness.
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Gradient Flow Sampler-based Distributionally Robust Optimization
Entropy-regularized Wasserstein DRO can be solved by sampling from a Gibbs worst-case distribution with gradient-flow samplers, giving new WFR/SVGD algorithms and a principled recovery of WRM.
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Extreme Event Aware ($\eta$-) Learning
η-learning adds a 1-Wasserstein penalty matching a model's output distribution to a prescribed reference distribution so the model can generate extreme events absent from its training data.
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Wasserstein Gradient Flows for Scalable and Regularized Barycenter Computation
A mini-batch Wasserstein gradient-flow algorithm computes scalable and label-aware Wasserstein barycenters, with empirical gains on domain adaptation.
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SoK: Stablecoins for Digital Transformation -- Design, Metrics, and Application with Real World Asset Tokenization as a Case Study
The paper presents a taxonomy, stakeholder-oriented evaluation framework, and an open-source benchmarking pipeline for stablecoin systems, illustrated with a real-world asset tokenization case study.
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Measuring Time-Series Dataset Similarity using Wasserstein Distance
Time-series dataset similarity is defined via the Wasserstein distance between fitted multivariate normal distributions, and the distance shows partial correlation with foundation model inference loss.
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