Related papers: An Agglomerative Clustering of Simulation Output D…
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…
We consider a general online stochastic optimization problem with multiple budget constraints over a horizon of finite time periods. In each time period, a reward function and multiple cost functions are revealed, and the decision maker…
Distributional (or distribution-valued) data are a new type of data arising from several sources and are considered as realizations of distributional variables. A new set of fuzzy c-means algorithms for data described by distributional…
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…
The following working document summarizes our work on the clustering of financial time series. It was written for a workshop on information geometry and its application for image and signal processing. This workshop brought several experts…
We consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset. Using the Wasserstein metric, we construct a ball in the space of (multivariate and non-discrete)…
This paper presents a unified approach based on Wasserstein distance to derive concentration bounds for empirical estimates for two broad classes of risk measures defined in the paper. The classes of risk measures introduced include as…
This paper investigates the robust optimal control of sampled-data stochastic systems with multiplicative noise and distributional ambiguity. We consider a class of discrete-time optimal control problems where the controller \emph{jointly}…
Modeling observations as random distributions embedded within Wasserstein spaces is becoming increasingly popular across scientific fields, as it captures the variability and geometric structure of the data more effectively. However, the…
We study the problem of model aggregation within the Wasserstein space for probability measures on the real line. Given a fixed finite collection of candidate probability models, we consider the associated class of Wasserstein barycenters…
We study data-driven decision problems where historical observations are generated by a time-evolving distribution whose consecutive shifts are bounded in Wasserstein distance. We address this nonstationarity using a distributionally robust…
Model-based clustering is widely-used in a variety of application areas. However, fundamental concerns remain about robustness. In particular, results can be sensitive to the choice of kernel representing the within-cluster data density.…
Nowadays stochastic computer simulations with both numeral and distribution inputs are widely used to mimic complex systems which contain a great deal of uncertainty. This paper studies the design and analysis issues of such computer…
We propose a computationally simple framework for clustering functional data based on Gaussian-process-generated random projections. In this approach, each curve is first projected onto a large collection of independent Gaussian process…
This paper presents a clustering technique that reduces the susceptibility to data noise by learning and clustering the data-distribution and then assigning the data to the cluster of its distribution. In the process, it reduces the impact…
Comparing probability distributions is at the crux of many machine learning algorithms. Maximum Mean Discrepancies (MMD) and Wasserstein distances are two classes of distances between probability distributions that have attracted abundant…
Agglomerative hierarchical clustering is one of the most widely used approaches for exploring how observations in a dataset relate to each other. However, its greedy nature makes it highly sensitive to small perturbations in the data, often…
The Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing distributions. It has found numerous applications in several hard problems, such as domain…
Optimal transport is a foundational problem in optimization, that allows to compare probability distributions while taking into account geometric aspects. Its optimal objective value, the Wasserstein distance, provides an important loss…
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…