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作者：Ho, Michael; Xin, Jack
作者单位：University of California System; University of California Irvine
摘要：Estimation of the covariance matrix of asset returns from high frequency data is complicated by asynchronous returns, market microstructure noise and jumps. One technique for addressing both asynchronous returns and market microstructure is the Kalman-Expectation-Maximization (KEM) algorithm. However the KEM approach assumes log-normal prices and does not address jumps in the return process which can corrupt estimation of the covariance matrix. In this paper we extend the KEM algorithm to pric...
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作者：Banert, Sebastian; Bot, Radu Ioan
作者单位：Royal Institute of Technology; University of Vienna
摘要：The possibilities of exploiting the special structure of d.c. programs, which consist of optimising the difference of convex functions, are currently more or less limited to variants of the DCA proposed by Pham Dinh Tao and Le Thi Hoai An in 1997. These assume that either the convex or the concave part, or both, are evaluated by one of their subgradients. In this paper we propose an algorithm which allows the evaluation of both the concave and the convex part by their proximal points. Addition...
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作者：Sun, Tianxiao; Quoc Tran-Dinh
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：We study the smooth structure of convex functions by generalizing a powerful concept so-called self-concordance introduced by Nesterov and Nemirovskii in the early 1990s to a broader class of convex functions which we call generalized self-concordant functions. This notion allows us to develop a unified framework for designing Newton-type methods to solve convex optimization problems. The proposed theory provides a mathematical tool to analyze both local and global convergence of Newton-type m...
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作者：Hajinezhad, Davood; Hong, Mingyi
作者单位：SAS Institute Inc; University of Minnesota System; University of Minnesota Twin Cities
摘要：In this paper, we propose a perturbed proximal primal-dual algorithm (PProx-PDA) for an important class of linearly constrained optimization problems, whose objective is the sum of smooth (possibly nonconvex) and convex (possibly nonsmooth) functions. This family of problems can be used to model many statistical and engineering applications, such as high-dimensional subspace estimation and the distributed machine learning. The proposed method is of the Uzawa type, in which a primal gradient de...
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作者：Aswani, Anil
作者单位：University of California System; University of California Berkeley
摘要：Much of statistics relies upon four key elements: a law of large numbers, a calculus to operationalize stochastic convergence, a central limit theorem, and a framework for constructing local approximations. These elements are well-understood for objects in a vector space (e.g., points or functions); however, much statistical theory does not directly translate to sets because they do not form a vector space. Building on probability theory for random sets, this paper uses variational analysis to...
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作者：Royset, Johannes O.
作者单位：United States Department of Defense; United States Navy; Naval Postgraduate School
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作者：Liu, Yufeng; Pang, Jong-Shi; Xin, Jack
作者单位：University of North Carolina; University of North Carolina Chapel Hill; University of Southern California; University of California System; University of California Irvine
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作者：Norton, Matthew; Uryasev, Stan
作者单位：United States Department of Defense; United States Navy; Naval Postgraduate School; State University System of Florida; University of Florida
摘要：In binary classification, performance metrics that are defined as the probability that some error exceeds a threshold are numerically difficult to optimize directly and also hide potentially important information about the magnitude of errors larger than the threshold. Defining similar metrics, instead, using Buffered Probability of Exceedance (bPOE) generates counterpart metrics that resolve both of these issues. We apply this approach to the case of AUC, the Area Under the ROC curve, and def...
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作者：Schoepfer, Frank; Lorenz, Dirk A.
作者单位：Carl von Ossietzky Universitat Oldenburg; Braunschweig University of Technology
摘要：The randomized version of the Kaczmarz method for the solution of consistent linear systems is known to converge linearly in expectation. And even in the possibly inconsistent case, when only noisy data is given, the iterates are expected to reach an error threshold in the order of the noise-level with the same rate as in the noiseless case. In this work we show that the same also holds for the iterates of the recently proposed randomized sparse Kaczmarz method for recovery of sparse solutions...
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作者：Kim, Jinhak; Tawarmalani, Mohit; Richard, Jean-Philippe P.
作者单位：University of South Alabama; Purdue University System; Purdue University; State University System of Florida; University of Florida
摘要：We derive cutting planes for cardinality-constrained linear programs. These inequalities can be used to separate any basic feasible solution of an LP relaxation of the problem, assuming that this solution violates the cardinality requirement. To derive them, we first relax the given simplex tableau into a disjunctive set, expressed in the space of nonbasic variables. We establish that coefficients of valid inequalities for the closed convex hull of this set obey ratios that can be computed dir...
