Related papers: Support points
We study configurations of points on the unit sphere that minimize potential energy for a broad class of potential functions (viewed as functions of the squared Euclidean distance between points). Call a configuration sharp if there are m…
Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the probability mass of one distribution in…
We study the use of power weighted shortest path distance functions for clustering high dimensional Euclidean data, under the assumption that the data is drawn from a collection of disjoint low dimensional manifolds. We argue, theoretically…
We introduce the convex matching distance, a novel metric for comparing functions with values in the real plane. This metric measures the maximal bottleneck distance between the persistence diagrams associated with the convex combinations…
The paper introduces a special case of the Euclidean distance matrix completion problem (edmcp) of interest in statistical data analysis where only the minimal spanning tree distances are given and the matrix completion must preserve the…
Estimations of physical parameters using data usually involve non-uniform experimental efficiencies. In this article, a method of maximum likelihood fit is introduced using the efficiency as a weight, while the probability distribution…
Estimating copulas with discrete marginal distributions is challenging, especially in high dimensions, because computing the likelihood contribution of each observation requires evaluating $2^{J}$ terms, with $J$ the number of discrete…
Context: Two-point correlation functions are used throughout cosmology as a measure for the statistics of random fields. When used in Bayesian parameter estimation, their likelihood function is usually replaced by a Gaussian approximation.…
Scenario reduction techniques are widely applied for solving sophisticated dynamic and stochastic programs, especially in energy and power systems, but also used in probabilistic forecasting, clustering and estimating generative adversarial…
Importance sampling is a Monte Carlo method which designs estimators of expectations under a target distribution using weighted samples from a proposal distribution. When the target distribution is complex, such as multimodal distributions…
We consider the Monge problem of optimal transport between a compactly supported source measure and a target probability measure with unbounded support. We consider the convergence of optimal maps and potential functions when the target…
Many machine learning applications require operating on a spatially distributed dataset. Despite technological advances, privacy considerations and communication constraints may prevent gathering the entire dataset in a central unit. In…
Population Monte Carlo (PMC) sampling methods are powerful tools for approximating distributions of static unknowns given a set of observations. These methods are iterative in nature: at each step they generate samples from a proposal…
We propose a new approximate method for counting the number of the solutions for constraint satisfaction problem (CSP). The method derives from the partition function based on introducing the free energy and capturing the relationship of…
In this paper, we study the problem of finding the Euclidean distance to a convex cone generated by a set of discrete points in $\mathbb{R}^n_+$. In particular, we are interested in problems where the discrete points are the set of feasible…
We introduce a novel Entropy-driven Monte Carlo (EdMC) strategy to efficiently sample solutions of random Constraint Satisfaction Problems (CSPs). First, we extend a recent result that, using a large-deviation analysis, shows that the…
Distance-based tests, also called "energy statistics", are leading methods for two-sample and independence tests from the statistics community. Kernel-based tests, developed from "kernel mean embeddings", are leading methods for two-sample…
Aims. Numerical test-particle simulations are a reliable and frequently used tool to test analytical transport theories and to predict mean-free paths. The comparison between solutions of the diffusion equation and the particle flux is used…
Statisticians often use Monte Carlo methods to approximate probability distributions, primarily with Markov chain Monte Carlo and importance sampling. Sequential Monte Carlo samplers are a class of algorithms that combine both techniques to…
An efficient Path Integral Monte Carlo procedure is proposed to simulate the behavior of quantum many-body dissipative systems described within the framework of the influence functional. Thermodynamic observables are obtained by Monte Carlo…