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Adaptive robust optimization problems are usually solved approximately by restricting the adaptive decisions to simple parametric decision rules. However, the corresponding approximation error can be substantial. In this paper we show that…
In this work clustering schemes for uncertain and structured data are considered relying on the notion of Wasserstein barycenters, accompanied by appropriate clustering indices based on the intrinsic geometry of the Wasserstein space where…
We consider the following multi-component sparse PCA problem: given a set of data points, we seek to extract a small number of sparse components with disjoint supports that jointly capture the maximum possible variance. These components can…
Biclustering, also known as co-clustering or two-way clustering, simultaneously partitions the rows and columns of a data matrix to reveal submatrices with coherent patterns. Incorporating background knowledge into clustering to enhance…
The energy landscape of high-dimensional non-convex optimization problems is crucial to understanding the effectiveness of modern deep neural network architectures. Recent works have experimentally shown that two different solutions found…
B\'ezier simplex fitting algorithms have been recently proposed to approximate the Pareto set/front of multi-objective continuous optimization problems. These new methods have shown to be successful at approximating various shapes of Pareto…
Variational problems that involve Wasserstein distances and more generally optimal transport (OT) theory are playing an increasingly important role in data sciences. Such problems can be used to form an examplar measure out of various…
We study the problem of distributional matrix completion: Given a sparsely observed matrix of empirical distributions, we seek to impute the true distributions associated with both observed and unobserved matrix entries. This is a…
We study the problem of estimating precision matrices in Gaussian distributions that are multivariate totally positive of order two ($\mathrm{MTP}_2$). The precision matrix in such a distribution is an M-matrix. This problem can be…
In this paper, we study the problem of sampling from a given probability density function that is known to be smooth and strongly log-concave. We analyze several methods of approximate sampling based on discretizations of the (highly…
Motivated by the Bures distance, we introduce a new family of distances, \emph{relative translation invariant Wasserstein distances}, denoted by $RW_p$, as an extension of the classical Wasserstein distances $W_p$ for $p \in [1, +\infty)$.…
A randomized version of the recently developed barycenter method for derivative-free optimization has desirable properties of a gradient search. We develop a complex version to avoid evaluations at high-gradient points. The method,…
The clustering problem, and more generally, latent factor discovery --or latent space inference-- is formulated in terms of the Wasserstein barycenter problem from optimal transport. The objective proposed is the maximization of the…
A randomized version of the recently developed barycenter method for derivative--free optimization has desirable properties of a gradient search. We developed a complex version to avoid evaluations at high--gradient points. The method,…
Distributed systems require fusing heterogeneous local probability distributions into a global summary over sparse and unreliable communication networks. Traditional consensus algorithms, which average distributions in Euclidean space,…
We consider a multimarginal optimal transport, which includes as a particular case the Wasserstein barycenter problem. In this problem one has to find an optimal coupling between $m$ probability measures, which amounts to finding a tensor…
Optimal transport has gained significant attention in recent years due to its effectiveness in deep learning and computer vision. Its descendant metric, the Wasserstein distance, has been particularly successful in measuring distribution…
Computing the optimal transport distance between statistical distributions is a fundamental task in machine learning. One remarkable recent advancement is entropic regularization and the Sinkhorn algorithm, which utilizes only matrix…
Scaling algorithms for entropic transport-type problems have become a very popular numerical method, encompassing Wasserstein barycenters, multi-marginal problems, gradient flows and unbalanced transport. However, a standard implementation…
Barycenter problems encode important geometric information about a metric space. While these problems are typically studied with positive weight coefficients associated to each distance term, more general signed Wasserstein barycenter…