Related papers: Wide Consensus for Parallelized Inference
Wasserstein barycenters provide a geometric notion of the weighted average of probability measures based on optimal transport. In this paper, we present a scalable algorithm to compute Wasserstein-2 barycenters given sample access to the…
This paper proposes a new distance metric between clusterings that incorporates information about the spatial distribution of points and clusters. Our approach builds on the idea of a Hilbert space-based representation of clusters as a…
This study focuses on finite-sample inference on the non-linear Bures-Wasserstein manifold and introduces a generalized bootstrap procedure for estimating Bures-Wasserstein barycenters. We provide non-asymptotic statistical guarantees for…
The design of sensor networks capable of reaching a consensus on a globally optimal decision test, without the need for a fusion center, is a problem that has received considerable attention in the last years. Many consensus algorithms have…
We address the problem of finding a "best" deterministic query answer to a query over a probabilistic database. For this purpose, we propose the notion of a consensus world (or a consensus answer) which is a deterministic world (answer)…
We develop an estimator-based stochastic fixed-point framework for approximately computing the 2-Wasserstein barycenter of continuous, non-parametric probability measures. Notably, we provide the first rigorous convergence analysis for…
Consensus clustering fuses diverse basic partitions (i.e., clustering results obtained from conventional clustering methods) into an integrated one, which has attracted increasing attention in both academic and industrial areas due to its…
Let $\mathcal{P}_{2,ac}$ be the set of Borel probabilities on $\mathbb{R}^d$ with finite second moment and absolutely continuous with respect to Lebesgue measure. We consider the problem of finding the barycenter (or Fr\'echet mean) of a…
The Wasserstein distance is a distance between two probability distributions and has recently gained increasing popularity in statistics and machine learning, owing to its attractive properties. One important approach to extending this…
Wasserstein barycenter is the centroid of a collection of discrete probability distributions which minimizes the average of the $\ell_2$-Wasserstein distance. This paper focuses on the computation of Wasserstein barycenters under the case…
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…
Estimation of parameters that obey specific constraints is crucial in statistics and machine learning; for example, when parameters are required to satisfy boundedness, monotonicity, or linear inequalities. Traditional approaches impose…
We study the computation of doubly regularized Wasserstein barycenters, a recently introduced family of entropic barycenters governed by inner and outer regularization strengths. Previous research has demonstrated that various…
Conformal prediction yields a prediction set with guaranteed $1-\alpha$ coverage of the true target under the i.i.d. assumption, which may not hold and lead to a gap between $1-\alpha$ and the actual coverage. Prior studies bound the gap…
This paper presents a unified computational framework for the estimation of distances, geodesics and barycenters of merge trees. We extend recent work on the edit distance [106] and introduce a new metric, called the Wasserstein distance…
Distributed optimization algorithms have been studied extensively in the literature; however, underlying most algorithms is a linear consensus scheme, i.e. averaging variables from neighbors via doubly stochastic matrices. We consider…
We develop a novel clustering method for distributional data, where each data point is regarded as a probability distribution on the real line. For distributional data, it has been challenging to develop a clustering method that utilizes…
Inspired by recent advances in distributed algorithms for approximating Wasserstein barycenters, we propose a novel distributed algorithm for this problem. The main novelty is that we consider time-varying computational networks, which are…
If the prior probability distributions of all possible hypothetical true means and all possible observed means of a continuous variable are conditional on the universal set of all numbers (i.e., before the nature of a study is known and a…
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…