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作者：Sarkar, Purnamrita; Bickel, Peter J.
作者单位：University of Texas System; University of Texas Austin; University of California System; University of California Berkeley
摘要：Spectral clustering is a technique that clusters elements using the top few eigenvectors of their (possibly normalized) similarity matrix. The quality of spectral clustering is closely tied to the convergence properties of these principal eigenvectors. This rate of convergence has been shown to be identical for both the normalized and unnormalized variants in recent random matrix theory literature. However, normalization for spectral clustering is commonly believed to be beneficial [Stat. Comp...
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作者：Byrne, Simon; Dawid, A. Philip
作者单位：University of London; University College London; University of Cambridge
摘要：This paper considers the problem of defining distributions over graphical structures. We propose an extension of the hyper Markov properties of Dawid and Lauritzen [Ann. Statist. 21 (1993) 1272-1317], which we term structural Markov properties, for both undirected decomposable and directed acyclic graphs, which requires that the structure of distinct components of the graph be conditionally independent given the existence of a separating component. This allows the analysis and comparison of mu...
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作者：Maathuis, Marloes H.; Colombo, Diego
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We generalize Pearl's back-door criterion for directed acyclic graphs (DAGs) to more general types of graphs that describe Markov equivalence classes of DAGs and/or allow for arbitrarily many hidden variables. We also give easily checkable necessary and sufficient graphical criteria for the existence of a set of variables that satisfies our generalized back-door criterion, when considering a single intervention and a single outcome variable. Moreover, if such a set exists, we provide an explic...
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作者：Bhattacharyya, Sharmodeep; Bickel, Peter J.
作者单位：University of California System; University of California Berkeley; Oregon State University
摘要：Analysis of stochastic models of networks is quite important in light of the huge influx of network data in social, information and bio sciences, but a proper statistical analysis of features of different stochastic models of networks is still underway. We propose bootstrap subsampling methods for finding empirical distribution of count features or moments (Bickel, Chen and Levina [Ann. Statist. 39 (2011) 2280-2301]) and smooth functions of these features for the networks. Using these methods,...
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作者：Steinwart, Ingo
作者单位：University of Stuttgart
摘要：The clusters of a distribution are often defined by the connected components of a density level set. However, this definition depends on the user-specified level. We address this issue by proposing a simple, generic algorithm, which uses an almost arbitrary level set estimator to estimate the smallest level at which there are more than one connected components. In the case where this algorithm is fed with histogram-based level set estimates, we provide a finite sample analysis, which is then u...
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作者：Jacob, Pierre E.; Thiery, Alexandre H.
作者单位：University of Oxford; National University of Singapore
摘要：We study the existence of algorithms generating almost surely nonnegative unbiased estimators. We show that given a nonconstant real-valued function f and a sequence of unbiased estimators of lambda is an element of R, there is no algorithm yielding almost surely nonnegative unbiased estimators of f(lambda) is an element of R+. The study is motivated by pseudo-marginal Monte Carlo algorithms that rely on such nonnegative unbiased estimators. These methods allow exact inference in intractable m...
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作者：Ferreira, Ana; de Haan, Laurens
作者单位：Universidade de Lisboa; Universidade de Lisboa; Erasmus University Rotterdam; Erasmus University Rotterdam - Excl Erasmus MC
摘要：In extreme value theory, there are two fundamental approaches, both widely used: the block maxima (BM) method and the peaks-over-threshold (POT) method. Whereas much theoretical research has gone into the POT method, the BM method has not been studied thoroughly. The present paper aims at providing conditions under which the BM method can be justified. We also provide a theoretical comparative study of the methods, which is in general consistent with the vast literature on comparing the method...
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作者：Nickl, Richard
作者单位：University of Cambridge
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作者：Fan, Jianqing; Xue, Lingzhou; Zou, Hui
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; University of Minnesota System; University of Minnesota Twin Cities
