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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：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...
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作者：Chang, Chih-Hao; Huang, Hsin-Cheng; Ing, Ching-Kang
作者单位：National University Kaohsiung; Academia Sinica - Taiwan
摘要：Information criteria, such as Akaike's information criterion and Bayesian information criterion are often applied in model selection. However, their asymptotic behaviors for selecting geostatistical regression models have not been well studied, particularly under the fixed domain asymptotic framework with more and more data observed in a bounded fixed region. In this article, we study the generalized information criterion (GIC) for selecting geostatistical regression models under a more genera...
