论文检索

连续索引图模型AI 解读

Abstract Let X={Xu}u∈U be a real-valued Gaussian process indexed by a set U. We show that X can be viewed as a graphical model with an uncountably infinite graph, where each Xu is a vertex. This graph is characterized by the reproducing property of X’s covariance kernel, without restricting U to be finite or countable, allowing the modelling of stochastic processes in continuous time/space. Unlike traditional methods, this characterization is not based on zero entries of an…

通过最优传输映射进行分布对分布回归AI 解读

Summary We present a framework for performing regression when both covariate and response are probability distributions on a compact interval. Our regression model is based on the theory of optimal transportation, and links the conditional Fréchet mean of the response to the covariate via an optimal transport map. We define a Fréchet-least-squares estimator of this regression map, and establish its consistency and rate of convergence to the true map, under both full and…