Related papers: Generative modeling with low-rank Wasserstein poly…

A spline chaos expansion, referred to as SCE, is introduced for uncertainty quantification analysis. The expansion provides a means for representing an output random variable of interest with respect to multivariate orthonormal basis…

Distributional causal inference requires estimating not only average treatment effects but also interventional outcome distributions, including quantiles, tail risks, and policy-dependent uncertainty. As a method for distributional causal…

Many numerical and learning algorithms rely on the solution of the Monge-Kantorovich problem and Wasserstein distances, which provide appropriate distributional metrics. While the natural approach is to treat the problem as an…

The Wasserstein distance has emerged as a key metric to quantify distances between probability distributions, with applications in various fields, including machine learning, control theory, decision theory, and biological systems.…

As non-institutive polynomial chaos expansion (PCE) techniques have gained growing popularity among researchers, we here provide a comprehensive review of major sampling strategies for the least squares based PCE. Traditional sampling…

In many applications in statistics and machine learning, the availability of data samples from multiple possibly heterogeneous sources has become increasingly prevalent. On the other hand, in distributionally robust optimization, we seek…

Numerical simulation of stochastic differential equations over long time intervals poses significant computational challenges. In this paper, we propose a novel recursive polynomial chaos evolution method that achieves model reduction…

This paper is concerned by statistical inference problems from a data set whose elements may be modeled as random probability measures such as multiple histograms or point clouds. We propose to review recent contributions in statistics on…

The challenges for non-intrusive methods for Polynomial Chaos modeling lie in the computational efficiency and accuracy under a limited number of model simulations. These challenges can be addressed by enforcing sparsity in the series…

Gradient flow in the 2-Wasserstein space is widely used to optimize functionals over probability distributions and is typically implemented using an interacting particle system with $n$ particles. Analyzing these algorithms requires showing…

In this paper, a risk-aware motion control scheme is considered for mobile robots to avoid randomly moving obstacles when the true probability distribution of uncertainty is unknown. We propose a novel model predictive control (MPC) method…

We develop a foundational framework for inverse problems governed by evolutionary partial differential equations (PDEs) on the Wasserstein space of probability measures. While the forward problems for such transport-type PDEs have been…

Bayesian analysis enables combining prior knowledge with measurement data to learn model parameters. Commonly, one resorts to computing the maximum a posteriori (MAP) estimate, when only a point estimate of the parameters is of interest. We…

In the field of modern high-energy physics research, there is a growing emphasis on utilizing deep learning techniques to optimize event simulation, thereby expanding the statistical sample size for more accurate physical analysis.…

This paper provides a simple procedure to fit generative networks to target distributions, with the goal of a small Wasserstein distance (or other optimal transport costs). The approach is based on two principles: (a) if the source…

Learning disentangled representations leads to interpretable models and facilitates data generation with style transfer, which has been extensively studied on static data such as images in an unsupervised learning framework. However, only a…

Wasserstein Discriminant Analysis (WDA) is a new supervised method that can improve classification of high-dimensional data by computing a suitable linear map onto a lower dimensional subspace. Following the blueprint of classical Linear…

Building surrogate models with uncertainty quantification capabilities is essential for many engineering applications where randomness, such as variability in material properties, is unavoidable. Polynomial Chaos Expansion (PCE) is widely…

This paper presents a novel method for accelerating path planning tasks in unknown scenes with obstacles by utilizing Wasserstein Generative Adversarial Networks (WGANs) with Gradient Penalty (GP) to approximate the distribution of the free…

We study the problem of network regression, where one is interested in how the topology of a network changes as a function of Euclidean covariates. We build upon recent developments in generalized regression models on metric spaces based on…