相关论文: A Linear Transportation $\mathrm{L}^p$ Distance fo…
The Wasserstein distance is an attractive tool for data analysis but statistical inference is hindered by the lack of distributional limits. To overcome this obstacle, for probability measures supported on finitely many points, we derive…
We present a generalized optimal transport model in which the mass-preserving constraint for the $L^2$-Wasserstein distance is relaxed by introducing a source term in the continuity equation. The source term is also incorporated in the path…
Mixed-integer linear programming (MILP) is a powerful tool for addressing a wide range of real-world problems, but it lacks a clear structure for comparing instances. A reliable similarity metric could establish meaningful relationships…
We define a novel class of distances between statistical multivariate distributions by modeling an optimal transport problem on their marginals with respect to a ground distance defined on their conditionals. These new distances are metrics…
In this letter, we emulate real-world statistics for mobility patterns on road systems. We then propose modifications to the assumptions of the random waypoint (RWP) model to better represent high-mobility profiles. We call the model under…
Uniformity testing and the more general identity testing are well studied problems in distributional property testing. Most previous work focuses on testing under $L_1$-distance. However, when the support is very large or even continuous,…
This contribution features an accelerated computation of the Sinkhorn's algorithm, which approximates the Wasserstein transportation distance, by employing nonequispaced fast Fourier transforms (NFFT). The algorithm proposed allows…
The distance and divergence of the probability measures play a central role in statistics, machine learning, and many other related fields. The Wasserstein distance has received much attention in recent years because of its distinctions…
Distance measures between graphs are important primitives for a variety of learning tasks. In this work, we describe an unsupervised, optimal transport based approach to define a distance between graphs. Our idea is to derive…
Estimating the travel time for a given path is a fundamental problem in many urban transportation systems. However, prior works fail to well capture moving behaviors embedded in paths and thus do not estimate the travel time accurately. To…
Gaussian mixture models find their place as a powerful tool, mostly in the clustering problem, but with proper preparation also in feature extraction, pattern recognition, image segmentation and in general machine learning. When faced with…
We analyze the Wasserstein distance ($W$-distance) between two probability distributions associated with two multidimensional jump-diffusion processes. Specifically, we analyze a temporally decoupled squared $W_2$-distance, which provides…
We develop the theory of a metric, which we call the $\nu$-based Wasserstein metric and denote by $W_\nu$, on the set of probability measures $\mathcal P(X)$ on a domain $X \subseteq \mathbb{R}^m$. This metric is based on a slight…
We propose algorithms for sampling from posterior path measures $P(C([0, T], \mathbb{R}^d))$ under a general prior process. This leverages ideas from (1) controlled equilibrium dynamics, which gradually transport between two path measures,…
Remote sensing observations from satellites and global biogeochemical models have combined to revolutionize the study of ocean biogeochemical cycling, but comparing the two data streams to each other and across time remains challenging due…
A growing number of generative statistical models do not permit the numerical evaluation of their likelihood functions. Approximate Bayesian computation (ABC) has become a popular approach to overcome this issue, in which one simulates…
We develop a new class of distances for objects including lines, hyperplanes, and trajectories, based on the distance to a set of landmarks. These distances easily and interpretably map objects to a Euclidean space, are simple to compute,…
The Wasserstein metric or earth mover's distance (EMD) is a useful tool in statistics, machine learning and computer science with many applications to biological or medical imaging, among others. Especially in the light of increasingly…
In this work we study systems consisting of a group of moving particles. In such systems, often some important parameters are unknown and have to be estimated from observed data. Such parameter estimation problems can often be solved via a…
We present upper bounds for the Wasserstein distance of order $p$ between the marginals of L\'evy processes, including Gaussian approximations for jumps of infinite activity. Using the convolution structure, we further derive upper bounds…