3期

最新文章

• UNIVERSAL REGRESSION WITH ADVERSARIAL RESPONSES AI翻译
  作者：Blanchard, Moise; Jaillet, Patrick
  作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
  摘要：We provide algorithms for regression with adversarial responses under large classes of non-i.i.d. instance sequences, on general separable metric spaces, with provably minimal assumptions. We also give characterizations of learnability in this regression context. We consider universal consistency, which asks for strong consistency of a learner without restrictions on the value responses. Our analysis shows that such an objective is achievable for a significantly larger class of instance sequen...
• COMPLEXITY ANALYSIS OF BAYESIAN LEARNING OF HIGH-DIMENSIONAL DAG MODELS AND THEIR EQUIVALENCE CLASSES AI翻译
  作者：Zhou, Quan; Chang, Hyunwoong
  作者单位：Texas A&M University System; Texas A&M University College Station
  摘要：Structure learning via MCMC sampling is known to be very challenging because of the enormous search space and the existence of Markov equivalent DAGs. Theoretical results on the mixing behavior are lacking. In this work, we prove the rapid mixing of a random walk Metropolis-Hastings algorithm, which reveals that the complexity of Bayesian learning of sparse equivalence classes grows only polynomially in n and p, under some high-dimensional assumptions. A series of high-dimensional consistency ...
• OPTIMAL REACH ESTIMATION AND METRIC LEARNING AI翻译
  作者：Aamari, Eddie; Berenfeld, Clement; Levrard, Clement
  作者单位：Sorbonne Universite; Universite Paris Cite; University of Potsdam
  摘要：We study the estimation of the reach, an ubiquitous regularity parameter in manifold estimation and geometric data analysis. Given an i.i.d. sample vide optimal nonasymptotic bounds for the estimation of its reach. We build upon a formulation of the reach in terms of maximal curvature on one hand and geodesic metric distortion on the other. The derived rates are adaptive, with rates depending on whether the reach of M arises from curvature or from a bottleneck structure. In the process we deri...
• EFFICIENCY OF ESTIMATORS FOR LOCALLY ASYMPTOTICALLY NORMAL QUANTUM STATISTICAL MODELS AI翻译
  作者：Fujiwara, Akio; Yamagata, Koichi
  作者单位：University of Osaka; Research Organization of Information & Systems (ROIS); National Institute of Informatics (NII) - Japan
  摘要：We herein establish an asymptotic representation theorem for locally asymptotically normal quantum statistical models. This theorem enables us to study the asymptotic efficiency of quantum estimators, such as quantum regular estimators and quantum minimax estimators, leading to a universal tight lower bound beyond the i.i.d. assumption. This formulation complements the theory of quantum contiguity developed in the previous paper [Fujiwara and Yamagata, Bernoulli 26 (2020) 2105-2141], providing...
• OPTIMAL DISCRIMINANT ANALYSIS IN HIGH-DIMENSIONAL LATENT FACTOR MODELS AI翻译
  作者：Bing, Xin; Wegkamp, Marten
  作者单位：University of Toronto; Cornell University; Cornell University
  摘要：In high-dimensional classification problems, a commonly used approach is to first project the high-dimensional features into a lower-dimensional space, and base the classification on the resulting lower-dimensional projections. In this paper, we formulate a latent-variable model with a hidden lowdimensional structure to justify this two-step procedure and to guide which projection to choose. We propose a computationally efficient classifier that takes certain principal components (PCs) of the ...
• DISPERSAL DENSITY ESTIMATION ACROSS SCALES AI翻译
  作者：Hoffmann, Marc; Trabs, Mathias
  作者单位：Universite PSL; Universite Paris-Dauphine; Helmholtz Association; Karlsruhe Institute of Technology
  摘要：We consider a space structured population model generated by two-point clouds: a homogeneous Poisson process M with intensity n -> infinity as a model for a parent generation together with a Cox point process N as offspring generation, with conditional intensity given by the convolution of M with a scaled dispersal density sigma(-1)f (center dot /sigma). Based on a realisation of M and N, we study the nonparametric estimation of f and the estimation of the physical scale parameter sigma > 0 si...
• EXTREME VALUE INFERENCE FOR HETEROGENEOUS POWER LAW DATA AI翻译
  作者：Einmahl, John H. J.; He, Yi
  作者单位：Tilburg University; Tilburg University; University of Amsterdam
  摘要：We extend extreme value statistics to independent data with possibly very different distributions. In particular, we present novel asymptotic normality results for the Hill estimator, which now estimates the extreme value index of the average distribution. Due to the heterogeneity, the asymptotic variance can be substantially smaller than that in the i.i.d. case. As a special case, we consider a heterogeneous scales model where the asymptotic variance can be calculated explicitly. The primary ...
• OPTIMAL HIGH-DIMENSIONAL AND NONPARAMETRIC DISTRIBUTED TESTING UNDER COMMUNICATION CONSTRAINTS AI翻译
  作者：Szabo, Botond; Vuursteen, Lasse; van Zanten, Harry
  作者单位：Bocconi University; Delft University of Technology; Vrije Universiteit Amsterdam
  摘要：We derive minimax testing errors in a distributed framework where the data is split over multiple machines and their communication to a central ma-chine is limited to b bits. We investigate both the d- and infinite-dimensional signal detection problem under Gaussian white noise. We also derive dis-tributed testing algorithms reaching the theoretical lower bounds. Our results show that distributed testing is subject to fundamentally dif-ferent phenomena that are not observed in distributed esti...
• MINIMAX RATE OF DISTRIBUTION ESTIMATION ON UNKNOWN SUBMANIFOLDS UNDER ADVERSARIAL LOSSES AI翻译
  作者：Tang, Rong; Yang, Yun
  作者单位：Hong Kong University of Science & Technology; University of Illinois System; University of Illinois Urbana-Champaign
  摘要：Statistical inference from high-dimensional data with low-dimensional structures has recently attracted a lot of attention. In machine learning, deep generative modelling approaches implicitly estimate distributions of complex objects by creating new samples from the underlying distribution, and have achieved great success in generating synthetic realistic-looking images and texts. A key step in these approaches is the extraction of latent features or representations (encoding) that can be use...
• PAIRWISE INTERACTION FUNCTION ESTIMATION OF STATIONARY GIBBS POINT PROCESSES USING BASIS EXPANSION AI翻译
  作者：Ba, Ismaila; Coeurjolly, Jean-Francois; Cuevas-Pacheco, Francisco
  作者单位：University of Quebec; University of Quebec Montreal; Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); Inria; Universidad Tecnica Federico Santa Maria
  摘要：The class of Gibbs point processes (GPP) is a large class of spatial point processes able to model both clustered and repulsive point patterns. They are specified by their conditional intensity, which for a point pattern x and a loca-tion u, is roughly speaking the probability that an event occurs in an infinites-imal ball around u given the rest of the configuration is x. The most simple and natural class of models is the class of pairwise interaction point processes where the conditional int...