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作者：Binev, Peter; Cohen, Albert; Dahmen, Wolfgang; DeVore, Ronald
作者单位：University of South Carolina System; University of South Carolina Columbia; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); RWTH Aachen University; Texas A&M University System; Texas A&M University College Station
摘要：Algorithms for binary classification based on adaptive tree partitioning are formulated and analyzed for both their risk performance and their friendliness to numerical implementation. The algorithms can be-viewed as generating a set approximation to the Bayes set and thus fall into the general category of set estimators. In contrast with the most studied tree-based algorithms, which utilize piecewise constant approximation on the generated partition [IEEE Trans. Inform. Theory 52 (2006) 1335-...
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作者：Schervish, M. J.; Seidenfeld, Teddy; Kadane, J. B.
作者单位：Carnegie Mellon University; Carnegie Mellon University
摘要：We investigate differences between a simple Dominance Principle applied to sums of fair prices for variables and dominance applied to sums of forecasts for variables scored by proper scoring rules. In particular, we consider differences when fair prices and forecasts correspond to finitely additive expectations and dominance is applied with infinitely many prices and/or forecasts.
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作者：Li, Ke
作者单位：International Business Machines (IBM); IBM USA; Massachusetts Institute of Technology (MIT); National University of Singapore
摘要：In the asymptotic theory of quantum hypothesis testing, the minimal error probability of the first kind jumps sharply from zero to one when the error exponent of the second kind passes by the point of the relative entropy of the two states in an increasing way. This is well known as the direct part and strong converse of quantum Stein's lemma. Here we look into the behavior of this sudden change and have make it clear how the error of first kind grows smoothly according to a lower order of the...
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作者：Bertsimas, Dimitris; Mazumder, Rahul
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); Columbia University
摘要：We address the Least Quantile of Squares (LQS) (and in particular the Least Median of Squares) regression problem using modern optimization methods. We propose a Mixed Integer Optimization (MIO) formulation of the LQS problem which allows us to find a provably global optimal solution for the LQS problem. Our MIO framework has the appealing characteristic that if we terminate the algorithm early, we obtain a solution with a guarantee on its sub-optimality. We also propose continuous optimizatio...
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作者：Pazman, Andrej; Pronzato, Luc
作者单位：Comenius University Bratislava; Centre National de la Recherche Scientifique (CNRS); Universite Cote d'Azur
摘要：Among the major difficulties that one may encounter when estimating parameters in a nonlinear regression model are the nonuniqueness of the estimator, its instability with respect to small perturbations of the observations and the presence of local optimizers of the estimation criterion. We show that these estimability issues can be taken into account at the design stage, through the definition of suitable design criteria. Extensions of E-, c- and G-optimality criteria are considered, which wh...
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作者：Fan, Jianqing; Xue, Lingzhou; Zou, Hui
作者单位：Princeton University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; University of Minnesota System; University of Minnesota Twin Cities
摘要：Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimum computed by a given optimization algorithm possesses those nice theoretical properties. To close this importa...
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作者：Cai, T. Tony; Yuan, Ming
作者单位：University of Pennsylvania; University of Wisconsin System; University of Wisconsin Madison
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作者：Whiteley, Nick; Lee, Anthony
作者单位：University of Bristol; University of Warwick
摘要：We investigate sampling laws for particle algorithms and the influence of these laws on the efficiency of particle approximations of marginal likelihoods in hidden Markov models. Among a broad class of candidates we characterize the essentially unique family of particle system transition kernels which is optimal with respect to an asymptotic-in-time variance growth rate criterion. The sampling structure of the algorithm defined by these optimal transitions turns out to be only subtly different...
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作者：Fasy, Brittany Terese; Lecci, Fabrizio; Rinaldo, Alessandro; Wasserman, Larry; Balakrishnan, Sivaraman; Singh, Aarti
作者单位：Tulane University; Carnegie Mellon University; Carnegie Mellon University
摘要：Persistent homology is a method for probing topological properties of point clouds and functions. The method involves tracking the birth and death of topological features (2000) as one varies a tuning parameter. Features with short lifetimes are informally considered to be topological noise, and those with a long lifetime are considered to be topological signal. In this paper, we bring some statistical ideas to persistent homology. In particular, we derive confidence sets that allow us to sepa...
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作者：Wang, Zhaoran; Liu, Han; Zhang, Tong
作者单位：Princeton University; Rutgers University System; Rutgers University New Brunswick
摘要：We provide theoretical analysis of the statistical and computational properties of penalized M-estimators that can be formulated as the solution to a possibly nonconvex optimization problem. Many important estimators fall in this category, including least squares regression with nonconvex regularization, generalized linear models with nonconvex.regularization and sparse elliptical random design regression. For these problems, it is intractable to calculate the global solution due to the noncon...
