Related papers: A sliced Wasserstein and diffusion approach to ran…
We propose a methodology for intercomparing climate models and evaluating their performance against benchmarks based on the use of the Wasserstein distance (WD). This distance provides a rigorous way to measure quantitatively the difference…
We study the decentralized distributed computation of discrete approximations for the regularized Wasserstein barycenter of a finite set of continuous probability measures distributedly stored over a network. We assume there is a network of…
We present discretize_distributions, a Python package that efficiently constructs discrete approximations of Gaussian mixture distributions and provides guarantees on the approximation error in Wasserstein distance. The package implements…
The prior distribution is a crucial building block in Bayesian analysis, and its choice will impact the subsequent inference. It is therefore important to have a convenient way to quantify this impact, as such a measure of prior impact will…
We address the challenge of sequential data-driven decision-making under context distributional uncertainty. This problem arises in numerous real-world scenarios where the learner optimizes black-box objective functions in the presence of…
In this paper, we propose a distributed algorithm for the minimum dominating set problem. For some especial networks, we prove theoretically that the achieved answer by our proposed algorithm is a constant approximation factor of the exact…
Regression analysis with probability measures as input predictors and output response has recently drawn great attention. However, it is challenging to handle multiple input probability measures due to the non-flat Riemannian geometry of…
The sliced-Wasserstein flow is an evolution equation where a probability density evolves in time, advected by a velocity field computed as the average among directions in the unit sphere of the optimal transport displacements from its 1D…
We propose a variational approach to approximate measures with measures uniformly distributed over a 1 dimentional set. The problem consists in minimizing a Wasserstein distance as a data term with a regularization given by the length of…
Sliced Wasserstein (SW) distance has been widely used in different application scenarios since it can be scaled to a large number of supports without suffering from the curse of dimensionality. The value of sliced Wasserstein distance is…
In this paper we introduce some recent progresses on the convergence rate in Wasserstein distance for empirical measures of Markov processes. For diffusion processes on compact manifolds possibly with reflecting or killing boundary…
Composite quantile regression has been used to obtain robust estimators of regression coefficients in linear models with good statistical efficiency. By revealing an intrinsic link between the composite quantile regression loss function and…
Understanding the space of probability measures on a metric space equipped with a Wasserstein distance is one of the fundamental questions in mathematical analysis. The Wasserstein metric has received a lot of attention in the machine…
We consider statistical methods which invoke a min-max distributionally robust formulation to extract good out-of-sample performance in data-driven optimization and learning problems. Acknowledging the distributional uncertainty in learning…
Distribution matching is central to many vision and graphics tasks, where the widely used Wasserstein distance is too costly to compute for high dimensional distributions. The Sliced Wasserstein Distance (SWD) offers a scalable alternative,…
We obtain essentially matching upper and lower bounds for the expected max-sliced 1-Wasserstein distance between a probability measure on a separable Hilbert space and its empirical distribution from $n$ samples. By proving a Banach space…
Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…
We provide full theoretical guarantees for the convergence behaviour of diffusion-based generative models under the assumption of strongly log-concave data distributions while our approximating class of functions used for score estimation…
We provide convergence guarantees in Wasserstein distance for a variety of variance-reduction methods: SAGA Langevin diffusion, SVRG Langevin diffusion and control-variate underdamped Langevin diffusion. We analyze these methods under a…
Conditional distribution is a fundamental quantity for describing the relationship between a response and a predictor. We propose a Wasserstein generative approach to learning a conditional distribution. The proposed approach uses a…