The Annals of Applied Probability

最新文章

• STATISTICAL LIMITS OF CORRELATION DETECTION IN TREES AI翻译
  作者：Ganassali, Luca; Massoulie, Laurent; Semerjian, Guilhem
  作者单位：Universite PSL; Ecole Normale Superieure (ENS); Inria; Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Sorbonne Universite
  摘要：In this paper we address the problem of testing whether two observed trees (t, t') are sampled either independently or from a joint distribution under which they are correlated. This problem, which we refer to as correlation detection in trees, plays a key role in the study of graph alignment for two correlated random graphs. Motivated by graph alignment, we investigate the conditions of existence of one-sided tests, that is, tests which have vanishing type I error and nonvanishing power in th...
• CORRELATION DETECTION IN TREES FOR PLANTED GRAPH ALIGNMENT AI翻译
  作者：Ganassali, Luca; Lelarge, Marc; Massoulie, Laurent
  作者单位：Universite PSL; Ecole Normale Superieure (ENS); Inria
  摘要：Motivated by alignment of correlated sparse random graphs, we introduce a hypothesis testing problem of deciding whether or not two random trees are correlated. We study the likelihood ratio test and obtain sufficient conditions under which this task is impossible or feasible. We propose MPAlign, a message-passing algorithm for graph alignment inspired by the tree correlation detection problem. We prove MPAlign to succeed in polynomial time at partial alignment whenever tree detection is feasi...
• PROPAGATION OF CHAOS AND POISSON HYPOTHESIS FOR REPLICA MEAN-FIELD MODELS OF INTENSITY-BASED NEURAL NETWORKS AI翻译
  作者：Davydova, Michel
  作者单位：Inria; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS)
  摘要：Neural computations arising from myriads of interactions between spiking neurons can be modeled as network dynamics with punctuate interactions. However, most relevant dynamics do not allow for computational tractability. To circumvent this difficulty, the Poisson hypothesis regime replaces interaction times between neurons by Poisson processes. We prove that the Poisson hypothesis holds at the limit of an infinite number of replicas in the replica-mean-field model, which consists of randomly ...
• LARGE-DIMENSIONAL CENTRAL LIMIT THEOREM WITHFOURTH-MOMENT ERROR BOUNDS ON CONVEX SETS AND BALLS AI翻译
  作者：Fang, Xiao; Koike, Yuta
  作者单位：Chinese University of Hong Kong; University of Tokyo
  摘要：We prove the large-dimensional Gaussian approximation of a sum ofnindependent random vectors inRdtogether with fourth-moment error boundson convex sets and Euclidean balls. Our bounds have near-optimal depen-dence onnand, compared with classical third-moment bounds, can achieveimproved dependence on the dimensiond. For centered balls, we obtain anadditional error bound that has a sub-optimal dependence onn, but recoversthe known result of the validity of the Gaussian approximation if and onlyi...
• DIFFUSIVE LIMITS OF LIPSCHITZ FUNCTIONALS OF POISSON MEASURES AI翻译
  作者：Besancon, Eustache; Coutin, Laure; Decreusefond, Laurent; Moyal, Pascal
  作者单位：IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite de Lorraine
  摘要：Continuous time Markov Chains, Hawkes processes and many other interesting processes can be described as a solution of stochastic differential equations driven by Poisson measures. Previous works, using the Stein's method, give the convergence rate of a sequence of renormalized Poisson measures toward the Brownian motion in several distances, constructed on the model of the Kantorovitch Rubinstein (or Wasserstein-1) distance. We show that many operations (like time change, convolution) on cont...
• SPECTRAL TELESCOPE: CONVERGENCE RATE BOUNDS FOR RANDOM-SCAN GIBBS SAMPLERS BASED ON A HIERARCHICAL STRUCTURE AI翻译
  作者：Qin, Qian; Wang, Guanyang
  作者单位：University of Minnesota System; University of Minnesota Twin Cities; Rutgers University System; Rutgers University New Brunswick
  摘要：Random-scan Gibbs samplers possess a natural hierarchical structure. The structure connects Gibbs samplers targeting higher-dimensional distributions to those targeting lower-dimensional ones. This leads to a quasi-telescoping property of their spectral gaps. Based on this property, we derive three new bounds on the spectral gaps and convergence rates of Gibbs samplers on general domains. The three bounds relate a chain's spectral gap to, respectively, the correlation structure of the target d...
• SURFACE AREA AND VOLUME OF EXCURSION SETS OBSERVED ON POINT CLOUD BASED POLYTOPIC TESSELLATIONS AI翻译
  作者：Cotsakis, Ryan; Di Bernardino, Elena; Duval, Celine
  作者单位：Universite Cote d'Azur; Universite de Lille; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
  摘要：The excursion set of a C2 smooth random field carries relevant information in its various geometric measures. From a computational viewpoint, one never has access to the continuous observation of the excursion set, but rather to observations at discrete points in space. It has been reported that for specific regular lattices of points in dimensions 2 and 3, the usual approximation of the surface area of the excursions does not converge when the lattice becomes dense in the domain of observatio...
• GENERATING GALTON-WATSON TREES USING RANDOM WALKS AND PERCOLATION FOR THE GAUSSIAN FREE FIELD AI翻译
  作者：Drewitz, Alexander; Gallo, Gioele; Prevost, Alexis
  作者单位：University of Cologne; University of Geneva
  摘要：The study of Gaussian free field level sets on supercritical Galton- Watson trees has been initiated by Ab & auml;cherli and Sznitman in 2018. By means of entirely different tools, we continue this investigation and generalize their main result on the positivity of the associated percolation critical parameter h* to the setting of arbitrary supercritical offspring distribution and random conductances. In our setting, this establishes a rigorous proof of the physics literature mantra that posit...
• CONTROLLED MEASURE-VALUED MARTINGALES: A VISCOSITY SOLUTION APPROACH AI翻译
  作者：Cox, Alexander M. G.; Kallblad, Sigrid; Larsson, Martin; Svaluto-Ferro, Sara
  作者单位：University of Bath; Royal Institute of Technology; Carnegie Mellon University; University of Verona
  摘要：We consider a class of stochastic control problems where the state process is a probability measure -valued process satisfying an additional martingale condition on its dynamics, called measure -valued martingales (MVMs). We establish the classical results of stochastic control for these problems: specifically, we prove that the value function for the problem can be characterised as the unique solution to the Hamilton-Jacobi-Bellman equation in the sense of viscosity solutions. In order to pro...
• LIMIT DISTRIBUTIONS AND SENSITIVITY ANALYSIS FOR EMPIRICAL ENTROPIC OPTIMAL TRANSPORT ON COUNTABLE SPACES AI翻译
  作者：Hundrieser, Shayan; Klatt, Marcel; Munk, Axel
  作者单位：University of Gottingen
  摘要：For probability measures on countable spaces we derive distributional limits for empirical entropic optimal transport quantities. More precisely, we show that the empirical optimal transport plan weakly converges to a centered Gaussian process and that the empirical entropic optimal transport value is asymptotically normal. The results are valid for a large class of cost functions and generalize distributional limits for empirical entropic optimal transport quantities on finite spaces. Our pro...