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作者：Christgau, Alexander Mangulad; Petersen, Lasse; Hansen, Niels richard
作者单位：University of Copenhagen
摘要：Conditional local independence is an asymmetric independence relation among continuous time stochastic processes. It describes whether the evolu-tion of one process is directly influenced by another process given the histo-ries of additional processes, and it is important for the description and learn-ing of causal relations among processes. We develop a model-free framework for testing the hypothesis that a counting process is conditionally locally in-dependent of another process. To this end...
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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...
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作者：Berrett, Thomas B.; Samworth, Richard J.
作者单位：University of Warwick; University of Cambridge
摘要：We consider the estimation of two-sample integral functionals, of the type that occur naturally, for example, when the object of interest is a diver-gence between unknown probability densities. Our first main result is that, in wide generality, a weighted nearest neighbour estimator is efficient, in the sense of achieving the local asymptotic minimax lower bound. Moreover, we also prove a corresponding central limit theorem, which facilitates the con-struction of asymptotically valid confidenc...
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作者：Jiao, Yuling; Shen, Guohao; Liu, Yuanyuan; Huang, Jian
作者单位：Wuhan University; Hong Kong Polytechnic University; Chinese University of Hong Kong
摘要：We study the properties of nonparametric least squares regression using deep neural networks. We derive nonasymptotic upper bounds for the excess risk of the empirical risk minimizer of feedforward deep neural regression. Our error bounds achieve minimax optimal rate and improve over the exist-ing ones in the sense that they depend polynomially on the dimension of the predictor, instead of exponentially on dimension. We show that the neural regression estimator can circumvent the curse of dime...
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作者：Li, Mengchu; Berrett, Thomas B.; Yu, Yi
作者单位：University of Warwick
摘要：It is of soaring demand to develop statistical analysis tools that are robust against contamination as well as preserving individual data owners' privacy. In spite of the fact that both topics host a rich body of literature, to the best of our knowledge, we are the first to systematically study the connections between the optimality under Huber's contamination model and the local dif-ferential privacy (LDP) constraints.In this paper, we start with a general minimax lower bound result, which di...
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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...
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作者：Marion, Joe; Mathews, Joseph; Schmidler, Scott C.
作者单位：Duke University
摘要：We present bounds for the finite-sample error of sequential Monte Carlo samplers on static spaces. Our approach explicitly relates the performance of the algorithm to properties of the chosen sequence of distributions and mixing properties of the associated Markov kernels. This allows us to give the first finite-sample comparison to other Monte Carlo schemes. We obtain bounds for the complexity of sequential Monte Carlo approximations for a variety of target distributions such as finite spaces...
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作者：Buecher, Axel; Zanger, Leandra
作者单位：Heinrich Heine University Dusseldorf
摘要：Modeling univariate block maxima by the generalized extreme value dis-tribution constitutes one of the most widely applied approaches in extreme value statistics. It has recently been found that, for an underlying station-ary time series, respective estimators may be improved by calculating block maxima in an overlapping way. A proof of concept is provided that the lat-ter finding also holds in situations that involve certain piecewise stationari-ties. A weak convergence result for an empirica...
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作者：Bilodeau, Blair; Negrea, Jeffrey; Roy, Daniel M.
作者单位：University of Toronto; University of Waterloo
摘要：We consider prediction with expert advice when data are generated from distributions varying arbitrarily within an unknown constraint set. This semiadversarial setting includes (at the extremes) the classical i.i.d. setting, when the unknown constraint set is restricted to be a singleton, and the unconstrained adversarial setting, when the constraint set is the set of all distributions. The Hedge algorithm-long known to be minimax (rate) optimal in the adversarial regime-was recently shown to ...
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作者：Roettger, Frank; Engelke, Sebastian; Zwiernik, Piotr
作者单位：University of Geneva; University of Toronto
摘要：Positive dependence is present in many real world data sets and has appealing stochastic properties that can be exploited in statistical modeling and in estimation. In particular, the notion of multivariate total positivity of order 2 (MTP2) is a convex constraint and acts as an implicit regularizer in the Gaussian case. We study positive dependence in multivariate extremes and introduce EMTP2, an extremal version of MTP2. This notion turns out to appear prominently in extremes, and in fact, i...
