arXiv:2310. 09149v3 Announce Type: replace-cross Abstract: We study the approximation of probability measures in the Wasserstein-$p$ distance by structured classes of approximators, motivated by applications in imaging, machine learning, and physical measurement under sensor constraints.
arXiv:2609. 26647v1 Announce Type: cross Abstract: We study statistical rates in entropic optimal transport in the semi-discrete regime where one measure has finite support and the other is subGaussian.
arXiv:2608. 13201v1 Announce Type: cross Abstract: We develop the statistical and algorithmic theory of inverse optimal transport (IOT) under the feature-parameterized cost C_theta(i,j) = -theta^T phi(i,j).
arXiv:2608.24098v1 Announce Type: new Abstract: Uniform stability controls how much one training example can change the loss at any test point. A new logarithmic-free upper bound shows that a $\gamma...
Uniform stability controls how much one training example can change the loss at any test point. A new logarithmic-free upper bound shows that a $γ$-uniformly stable algorithm with loss in $[0,L]$ has...
arXiv:2609. 27008v1 Announce Type: cross Abstract: We study the long-time behavior of Wasserstein gradient flows for interaction energies \[ \mathsf E[\mu] = \frac12\iint_{M\times M}K(x,y)\,\mathrm d\mu(x)\,\mathrm d\mu(y) \] on a closed manifold $M$.
arXiv:2607. 15702v2 Announce Type: replace-cross Abstract: We develop a non-asymptotic approximation, sampling, and finite-iteration optimization theory for variational physics-informed approximation of uniformly monotone nonlinear multiscale elliptic equations.
arXiv:2610. 02663v1 Announce Type: cross Abstract: Despite the remarkable empirical success of flow-matching models, their statistical generalization guarantees remain underdeveloped.
arXiv:2610.27022v1 Announce Type: cross Abstract: We study Gaussian kernel approximation and regularized logistic classification on a connected compact smooth embedded manifold $X\subset\mathbb R^d$...
arXiv:2607. 07468v1 Announce Type: cross Abstract: We study the recovery of sparse functions from finite, noisy, and indirect observations in the framework of statistical inverse learning.
arXiv:2608. 15472v1 Announce Type: cross Abstract: The problem of networked information aggregation, studied in Kearns et al.
arXiv:2606. 07325v1 Announce Type: cross Abstract: We study the minimax rate of estimating a future value $\mu_{t_n+h}$ of a curve $t\mapsto\mu_t$ in the $2$-Wasserstein space $\mathcal{P}_2(\mathbb{R}^d)$ from finitely many noisy snapshots of its past, under an adiabatic bound $\|\nabla_t^k v\|\le\varepsilon$ on the $k$-th covariant derivative of the velocity field.