arXiv:2607. 24235v1 Announce Type: cross Abstract: Over the past 20 years, kernel discrepancies have been leveraged as a highly powerful tool for quantifying the disagreement of distributions, with numerous successful applications in two-sample, goodness-of-fit, and independence testing, among others.
arXiv:2409. 08469v4 Announce Type: replace-cross Abstract: We provide finite-particle convergence rates for the Stein Variational Gradient Descent (SVGD) algorithm in the Kernelized Stein Discrepancy ($\mathsf{KSD}$) and Wasserstein-2 metrics.
We develop a comprehensive theory for regularized M-estimation in reproducing kernel Hilbert spaces. Under mild conditions on the loss we establish existence and measurability of the estimator, covering a wide range of convex and non-convex losses, including bounded robust losses.
arXiv:2507. 12843v3 Announce Type: replace Abstract: Are two distributions close to each other with statistical significance?
arXiv:2201. 01973v3 Announce Type: replace-cross Abstract: The problem of linear predictions has been extensively studied for the past century under pretty generalized frameworks.
arXiv:2607. 20119v1 Announce Type: cross Abstract: We introduce the Directional Kernel Mean Difference (DKMD), a signed statistic for univariate distribution comparison that preserves the direction of distributional shifts.
arXiv:2607. 29245v1 Announce Type: cross Abstract: We study the expected improvement (EI) policy for minimizing a deterministic objective function $f$ on a nonempty compact set $\mathcal X \subset\mathbb R^d$.
arXiv:2607. 10592v1 Announce Type: new Abstract: Many geometric statistics and manifold learning pipelines routinely produce observations -- such as tangent vectors or local frames -- whose natural home is a varying family of fibers attached to different points of a base manifold, rather than a single shared vector space.
arXiv:2608. 13922v1 Announce Type: new Abstract: Detecting distributional changes in high dimension is difficult when neither the pre-change nor post-change density is parametrically specified.
arXiv:2004. 05813v3 Announce Type: replace-cross Abstract: Suppose that we are given independent, identically distributed random samples $x_1,\cdots,x_n$ from a mixture at most $k$ many $d$-dimensional spherical Gaussian distributions $\mu_1,\cdots,\mu_{k_0}$ of identical and known variance $\sigma^2$ in each coordinate, such that the minimum $\ell^2$ distance between two distinct centers $y_l$ and $y_j$ is greater than $2\Delta\sigma \min\{\sqrt{d},\sqrt k\}$, where $\Delta>C_0$, and $C_0$ is a sufficiently large universal constant.
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.
arXiv:2511. 11498v2 Announce Type: replace-cross Abstract: We consider the problems of \emph{learning} and \emph{testing} real-valued convex functions over Gaussian space.
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.