相关论文: Extensions with shrinking fibers

This paper studies iterative schemes for measure transfer and approximation problems, which are defined through a slicing-and-matching procedure. Similar to the sliced Wasserstein distance, these schemes benefit from the availability of…

The present paper provides a general formula for the dimension of spline space over T-meshes using smoothing cofactor-conformality method. And we introduce a new notion, Diagonalizable T-mesh, over which the dimension formula is only…

We consider measurable and topological dynamical systems over locally compact abelian groups. Our main observation relates convergence of Wiener-Wintner type averages to eigenvalues of the dynamical system in question. As a consequence we…

According to the Furstenberg-Zimmer structure theorem, every measure-preserving system has a maximal distal factor, and is weak mixing relative to that factor. Furstenberg and Katznelson used this structural analysis of measure-preserving…

We introduce a family of maps generating continued fractions where the digit $1$ in the numerator is replaced cyclically by some given non-negative integers $(N_1,\ldots,N_m)$. We prove the convergence of the given algorithm, and study the…

The article considers generic extensions of measure-preserving actions. We prove that the P-entropy of the generic extensions with finite P-entropy is infinite. This is exploited to obtain the result by Austin, Glasner, Thouvenot, and Weiss…

We prove that skew systems with a sufficiently expanding base have approximate exponential decay of correlations, meaning that the exponential rate is observed modulo an error. The fiber maps are only assumed to be Lipschitz regular and to…

Data unfolding -- the removal of noise or artifacts from measurements -- is a fundamental task across the experimental sciences. Of particular interest are applications in physics, where the dominant approach is Richardson-Lucy (RL)…

This paper explores the Riemannian geometry of the Wasserstein space of the circle, namely $P(S^{1})$, the set of probability measures on the unit circle endowed with the 2-Wasserstein metric. Building on the foundational work of Otto,…

Wasserstein projections in the convex order were first considered in the framework of weak optimal transport, and found application in various problems such as concentration inequalities and martingale optimal transport. In dimension one,…

The Wasserstein distance is a distance between two probability distributions and has recently gained increasing popularity in statistics and machine learning, owing to its attractive properties. One important approach to extending this…

Let $(X,d,m)$ be a proper, non-branching, metric measure space. We show existence and uniqueness of optimal transport maps for cost written as non-decreasing and strictly convex functions of the distance, provided $(X,d,m)$ satisfies a new…

Many engineering and physiological applications deal with situations when a fluid is moving in flexible tubes with elastic walls. In the real-life applications like blood flow, there is often an additional complexity of vorticity being…

Computing the unregularized Wasserstein barycenter for measure-valued data is a challenging optimization task. Recent algorithms have been tailored to either discrete measures as point clouds or continuous measures discretized on regular…

We propose an algorithmic framework for dataset normalization in data augmentation pipelines that preserves topological stability under non-uniform scaling transformations. Given a finite metric space \( X \subset \mathbb{R}^n \) with…

We prove that the sequence of marginals obtained from the iterations of the Sinkhorn algorithm or the iterative proportional fitting procedure (IPFP) on joint densities, converges to an absolutely continuous curve on the $2$-Wasserstein…

The sliced Wasserstein metric compares probability measures on $\mathbb{R}^d$ by taking averages of the Wasserstein distances between projections of the measures to lines. The distance has found a range of applications in statistics and…

We prove existence of (at most denumerable many) absolutely continuous invariant probability measures for random one-dimensional dynamical systems with asymptotic expansion. If the rate of expansion (Lyapunov exponents) is bounded away from…

Optimal transport (OT) provides powerful tools for comparing probability measures in various types. The Wasserstein distance which arises naturally from the idea of OT is widely used in many machine learning applications. Unfortunately,…

This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…