Related papers: Wasserstein Autoregressive Models for Density Time…
We develop a Bayesian median autoregressive (BayesMAR) model for time series forecasting. The proposed method utilizes time-varying quantile regression at the median, favorably inheriting the robustness of median regression in contrast to…
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…
This paper builds Wasserstein ambiguity sets for the unknown probability distribution of dynamic random variables leveraging noisy partial-state observations. The constructed ambiguity sets contain the true distribution of the data with…
Wasserstein geometry and information geometry are two important structures to be introduced in a manifold of probability distributions. Wasserstein geometry is defined by using the transportation cost between two distributions, so it…
Gradient boosting is a sequential ensemble method that fits a new weaker learner to pseudo residuals at each iteration. We propose Wasserstein gradient boosting, a novel extension of gradient boosting that fits a new weak learner to…
Wasserstein distributionally robust optimization offers a framework for model fitting in machine learning under potential shifts in the data distribution. We study a regularized variant of this problem in which entropic smoothing produces a…
We study multi-objective optimization over probability distributions in Wasserstein space. Recently, Nguyen et al. (2025) introduced Multiple Wasserstein Gradient Descent (MWGraD) algorithm, which exploits the geometric structure of…
This paper proposes a distributionally robust approach to logistic regression. We use the Wasserstein distance to construct a ball in the space of probability distributions centered at the uniform distribution on the training samples. If…
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…
Modeling nonstationary processes is of paramount importance to many scientific disciplines including environmental science, ecology, and finance, among others. Consequently, flexible methodology that provides accurate estimation across a…
We consider a data-driven robust hypothesis test where the optimal test will minimize the worst-case performance regarding distributions that are close to the empirical distributions with respect to the Wasserstein distance. This leads to 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…
Point processes are becoming very popular in modeling asynchronous sequential data due to their sound mathematical foundation and strength in modeling a variety of real-world phenomena. Currently, they are often characterized via intensity…
To consider model uncertainty in global Fr\'{e}chet regression and improve density response prediction, we propose a frequentist model averaging method. The weights are chosen by minimizing a cross-validation criterion based on Wasserstein…
In this paper, we establish sharp upper and lower bounds on the convergence rate of the empirical measures of point processes under the Wasserstein distance. To this end, we first introduce a new metric on the space of counting measures…
Wasserstein geometry and information geometry are two important structures introduced in a manifold of probability distributions. The former is defined by using the transportation cost between two distributions, so it reflects the metric…
While time series prediction is an important, actively studied problem, the predictive accuracy of time series models is complicated by non-stationarity. We develop a fast and effective approach to allow for non-stationarity in the…
Existing approaches to depth or disparity estimation output a distribution over a set of pre-defined discrete values. This leads to inaccurate results when the true depth or disparity does not match any of these values. The fact that this…
Model Updating is frequently used in Structural Health Monitoring to determine structures' operating conditions and whether maintenance is required. Data collected by sensors are used to update the values of some initially unknown…
We present Neural Autoregressive Distribution Estimation (NADE) models, which are neural network architectures applied to the problem of unsupervised distribution and density estimation. They leverage the probability product rule and a…