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作者：Ghoshdastidar, Debarghya; Dukkipati, Ambedkar
作者单位：Indian Institute of Science (IISC) - Bangalore
摘要：Hypergraph partitioning lies at the heart of a number of problems in machine learning and network sciences. Many algorithms for hypergraph partitioning have been proposed that extend standard approaches for graph partitioning to the case of hypergraphs. However, theoretical aspects of such methods have seldom received attention in the literature as compared to the extensive studies on the guarantees of graph partitioning. For instance, consistency results of spectral graph partitioning under t...
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作者：Datta, Abhirup; Zou, Hui
作者单位：Johns Hopkins University; University of Minnesota System; University of Minnesota Twin Cities
摘要：Much theoretical and applied work has been devoted to high-dimensional regression with clean data. However, we often face corrupted data in many applications where missing data and measurement errors cannot be ignored. Loh and Wainwright [Ann. Statist. 40 (2012) 1637-1664] proposed a non-convex modification of the Lasso for doing high-dimensional regression with noisy and missing data. It is generally agreed that the virtues of convexity contribute fundamentally the success and popularity of t...
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作者：Ning, Yang; Zhao, Tianqi; Liu, Han
作者单位：Cornell University; Princeton University
摘要：We propose a new inferential framework for high-dimensional semiparametric generalized linear models. This framework addresses a variety of challenging problems in high-dimensional data analysis, including incomplete data, selection bias and heterogeneity. Our work has three main contributions: (i) We develop a regularized statistical chromatography approach to infer the parameter of interest under the proposed semiparametric generalized linear model without the need of estimating the unknown ...
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作者：Pensky, Marianna
作者单位：State University System of Florida; University of Central Florida
摘要：The present paper considers the problem of estimating a linear functional Phi = integral(infinity)(-infinity) phi(x) f (x) dx of an unknown deconvolution density f on the basis of n i. i. d. observations, Y-1,..., Y-n of Y = theta +xi, where xi has a known pdf g, and f is the pdf of theta. The objective of the present paper is to develop the a general minimax theory of estimating Phi, and to relate this problem to estimation of functionals Phi(n) = n(-1) Sigma(n)(i=1) phi(theta(i)) in indirect...
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作者：Dereudre, David; Lavancier, Frederic
作者单位：Universite de Lille; Nantes Universite
摘要：Strong consistency of the maximum likelihood estimator (MLE) for parametric Gibbs point process models is established. The setting is very general. It includes pairwise pair potentials, finite and infinite multibody interactions and geometrical interactions, where the range can be finite or infinite. The Gibbs interaction may depend linearly or nonlinearly on the parameters, a particular case being hardcore parameters and interaction range parameters. As important examples, we deduce the consi...
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作者：Ning, Yang; Liu, Han
作者单位：Cornell University; Princeton University
摘要：We consider the problem of uncertainty assessment for low dimensional components in high dimensional models. Specifically, we propose a novel decorrelated score function to handle the impact of high dimensional nuisance parameters. We consider both hypothesis tests and confidence regions for generic penalized M-estimators. Unlike most existing inferential methods which are tailored for individual models, our method provides a general framework for high dimensional inference and is applicable t...
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作者：Bibinger, Markus; Jirak, Moritz; Vetter, Mathias
作者单位：Braunschweig University of Technology; University of Kiel
摘要：In this work, we develop change-point methods for statistics of highfrequency data. The main interest is in the volatility of an Ito semimartingale, the latter being discretely observed over a fixed time horizon. We construct a minimax-optimal test to discriminate continuous paths from paths with volatility jumps, and it is shown that the test can be embedded into a more general theory to infer the smoothness of volatilities. In a high-frequency setting, we prove weak convergence of the test s...
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作者：Belitser, Eduard
作者单位：Vrije Universiteit Amsterdam
摘要：In the mildly ill-posed inverse signal-in-white-noise model, we construct confidence sets as credible balls with respect to the empirical Bayes posterior resulting from a certain two-level hierarchical prior. The quality of the posterior is characterized by the contraction rate which we allow to be local, that is, depending on the parameter. The issue of optimality of the constructed confidence sets is addressed via a trade-off between its size (the local radial rate) and its coverage probabil...
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作者：Collier, Olivier; Comminges, Laetitia; Tsybakov, Alexandre B.
作者单位：Universite Paris Saclay; Universite PSL; Universite Paris-Dauphine; Institut Polytechnique de Paris; ENSAE Paris
摘要：For the Gaussian sequence model, we obtain nonasymptotic minimax rates of estimation of the linear, quadratic and the l(2)-norm functionals on classes of sparse vectors and construct optimal estimators that attain these rates. The main object of interest is the class B-0(s) of s-sparse vectors theta = (theta(1) (,...,) theta(d)), for which we also provide completely adaptive estimators (independent of s and of the noise variance sigma) having logarithmically slower rates than the minimax ones....
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作者：Gao, Chao; Ma, Zongming; Zhou, Harrison H.
作者单位：University of Chicago; University of Pennsylvania; Yale University
摘要：Canonical correlation analysis is a classical technique for exploring the relationship between two sets of variables. It has important applications in analyzing high dimensional datasets originated from genomics, imaging and other fields. This paper considers adaptive minimax and computationally tractable estimation of leading sparse canonical coefficient vectors in high dimensions. Under a Gaussian canonical pair model, we first establish separate minimax estimation rates for canonical coeffi...
