相关论文: Approximate Algorithms For $k$-Sparse Wasserstein …

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…

We consider the problem of clustering datasets in the presence of arbitrary outliers. Traditional clustering algorithms such as k-means and spectral clustering are known to perform poorly for datasets contaminated with even a small number…

We propose a simple and efficient clustering method for high-dimensional data with a large number of clusters. Our algorithm achieves high-performance by evaluating distances of datapoints with a subset of the cluster centres. Our…

Clustering problems such as $k$-Median, and $k$-Means, are motivated from applications such as location planning, unsupervised learning among others. In such applications, it is important to find the clustering of points that is not…

We propose a balanced coarsening scheme for multilevel hypergraph partitioning. In addition, an initial partitioning algorithm is designed to improve the quality of k-way hypergraph partitioning. By assigning vertex weights through the LPT…

This paper presents a practical global optimization algorithm for the K-center clustering problem, which aims to select K samples as the cluster centers to minimize the maximum within-cluster distance. This algorithm is based on a…

We propose a new minimum-distance estimator for linear random coefficient models. This estimator integrates the recently advanced sliced Wasserstein distance with the nearest neighbor methods, both of which enhance computational efficiency.…

In the standard planar $k$-center clustering problem, one is given a set $P$ of $n$ points in the plane, and the goal is to select $k$ center points, so as to minimize the maximum distance over points in $P$ to their nearest center. Here we…

We consider a general task called partial Wasserstein covering with the goal of providing information on what patterns are not being taken into account in a dataset (e.g., dataset used during development) compared with another dataset(e.g.,…

Among dissimilarities between probability distributions, the Kernel Stein Discrepancy (KSD) has received much interest recently. We investigate the properties of its Wasserstein gradient flow to approximate a target probability distribution…

We present and study a novel algorithm for the computation of 2-Wasserstein population barycenters of absolutely continuous probability measures on Euclidean space. The proposed method can be seen as a stochastic gradient descent procedure…

In this work we introduce the concept of Bures-Wasserstein barycenter $Q_*$, that is essentially a Fr\'echet mean of some distribution $\mathbb{P}$ supported on a subspace of positive semi-definite Hermitian operators $\mathbb{H}_{+}(d)$.…

In this work, we investigate the convergence properties of the backward regularized Wasserstein proximal (BRWP) method for sampling a target distribution. The BRWP approach can be shown as a semi-implicit time discretization for a…

In the past few years powerful generalizations to the Euclidean k-means problem have been made, such as Bregman clustering [7], co-clustering (i.e., simultaneous clustering of rows and columns of an input matrix) [9,18], and tensor…

We study a clustering problem where the goal is to maximize the coverage of the input points by $k$ chosen centers. Specifically, given a set of $n$ points $P \subseteq \mathbb{R}^d$, the goal is to pick $k$ centers $C \subseteq…

Optimal transport (OT) finds a least cost transport plan between two probability distributions using a cost matrix defined on pairs of points. Unlike standard OT, which infers unstructured pointwise mappings, low-rank optimal transport…

Motivated by the 2D class averaging problem in single-particle cryo-electron microscopy (cryo-EM), we present a k-means algorithm based on a rotationally-invariant Wasserstein metric for images. Unlike existing methods that are based on…

The diameter $k$-clustering problem is the problem of partitioning a finite subset of $\mathbb{R}^d$ into $k$ subsets called clusters such that the maximum diameter of the clusters is minimized. One early clustering algorithm that computes…

In many situations where the interest lies in identifying clusters one might expect that not all available variables carry information about these groups. Furthermore, data quality (e.g. outliers or missing entries) might present a serious…

Off-policy evaluation and learning are concerned with assessing a given policy and learning an optimal policy from offline data without direct interaction with the environment. Often, the environment in which the data are collected differs…