相关论文: Fast Wasserstein rates for estimating probability …
We develop a projected Wasserstein distance for the two-sample test, a fundamental problem in statistics and machine learning: given two sets of samples, to determine whether they are from the same distribution. In particular, we aim to…
Estimating a $d$-dimensional distribution $\mu$ by the empirical measure $\hat{\mu}_n$ of its samples is an important task in probability theory, statistics and machine learning. It is well known that $\mathbb{E}[\mathcal{W}_p(\hat{\mu}_n,…
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…
Wasserstein distributionally robust estimators have emerged as powerful models for prediction and decision-making under uncertainty. These estimators provide attractive generalization guarantees: the robust objective obtained from the…
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…
Graphs are playing a crucial role in different fields since they are powerful tools to unveil intrinsic relationships among signals. In many scenarios, an accurate graph structure representing signals is not available at all and that…
We consider the problem of estimating a structured multivariate density, subject to Markov conditions implied by an undirected graph. In the worst case, without Markovian assumptions, this problem suffers from the curse of dimensionality.…
Wasserstein distributionally robust optimization (DRO) aims to find robust and generalizable solutions by hedging against data perturbations in Wasserstein distance. Despite its recent empirical success in operations research and machine…
Data consisting of time-indexed distributions of cross-sectional or intraday returns have been extensively studied in finance, and provide one example in which the data atoms consist of serially dependent probability distributions.…
The Wasserstein distance is a metric on a space of probability measures that has seen a surge of applications in statistics, machine learning, and applied mathematics. However, statistical aspects of Wasserstein distances are bottlenecked…
Flow Matching, a promising approach in generative modeling, has recently gained popularity. Relying on ordinary differential equations, it offers a simple and flexible alternative to diffusion models, which are currently the…
Many studies have been conducted on flows of probability measures, often in terms of gradient flows. We utilize a generalized notion of derivatives with respect to time to model the instantaneous evolution of empirically observed…
Many decision problems in science, engineering and economics are affected by uncertain parameters whose distribution is only indirectly observable through samples. The goal of data-driven decision-making is to learn a decision from finitely…
Squared Wasserstein distance is a frequently used tool to measure discrepancy between probability distributions. This distance is typically computed between empirical measures of size $n$ from two underlying random samples. Unfortunately,…
Distributionally-robust optimization is often studied for a fixed set of distributions rather than time-varying distributions that can drift significantly over time (which is, for instance, the case in finance and sociology due to…
We address the problem of efficiently computing Wasserstein distances for multiple pairs of distributions drawn from a meta-distribution. To this end, we propose a fast estimation method based on regressing Wasserstein distance on sliced…
We propose a new statistical model, the spiked transport model, which formalizes the assumption that two probability distributions differ only on a low-dimensional subspace. We study the minimax rate of estimation for the Wasserstein…
This paper deals with the estimation of a probability measure on the real line from data observed with an additive noise. We are interested in rates of convergence for the Wasserstein metric of order $p\geq 1$. The distribution of the…
Estimating the density of a distribution from samples is a fundamental problem in statistics. In many practical settings, the Wasserstein distance is an appropriate error metric for density estimation. For example, when estimating…
In this paper, we consider the problem of propagating an uncertain distribution by a possibly non-linear function and quantifying the resulting uncertainty. We measure the uncertainty using the Wasserstein distance, and for a given input…