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作者：Atamturk, Alper; Gomez, Andres
作者单位：University of California System; University of California Berkeley; Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh
摘要：We study quadratic optimization with indicator variables and an M-matrix, i.e., a PSD matrix with non-positive off-diagonal entries, which arises directly in image segmentation and portfolio optimization with transaction costs, as well as a substructure of general quadratic optimization problems. We prove, under mild assumptions, that the minimization problem is solvable in polynomial time by showing its equivalence to a submodular minimization problem. To strengthen the formulation, we decomp...
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作者：Li, Chris Junchi; Wang, Mengdi; Liu, Han; Zhang, Tong
作者单位：Princeton University; Rutgers University System; Rutgers University New Brunswick
摘要：Principal component analysis (PCA) has been a prominent tool for high-dimensional data analysis. Online algorithms that estimate the principal component by processing streaming data are of tremendous practical and theoretical interests. Despite its rich applications, theoretical convergence analysis remains largely open. In this paper, we cast online PCA into a stochastic nonconvex optimization problem, and we analyze the online PCA algorithm as a stochastic approximation iteration. The stocha...
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作者：Taeb, Armeen; Chandrasekaran, Venkat
作者单位：California Institute of Technology; California Institute of Technology; California Institute of Technology
摘要：Latent or unobserved phenomena pose a significant difficulty in data analysis as they induce complicated and confounding dependencies among a collection of observed variables. Factor analysis is a prominent multivariate statistical modeling approach that addresses this challenge by identifying the effects of (a small number of) latent variables on a set of observed variables. However, the latent variables in a factor model are purely mathematical objects that are derived from the observed phen...
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作者：Junger, Michael; Vanderbeck, Francois
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作者：Fang, Ethan X.; Liu, Han; Toh, Kim-Chuan; Zhou, Wen-Xin
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Princeton University; National University of Singapore; University of California System; University of California San Diego
摘要：This paper studies the matrix completion problem under arbitrary sampling schemes. We propose a new estimator incorporating both max-norm and nuclear-norm regularization, based on which we can conduct efficient low-rank matrix recovery using a random subset of entries observed with additive noise under general non-uniform and unknown sampling distributions. This method significantly relaxes the uniform sampling assumption imposed for the widely used nuclear-norm penalized approach, and makes l...
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作者：Combettes, Patrick L.; Salzo, Saverio; Villa, Silvia
作者单位：North Carolina State University; Istituto Italiano di Tecnologia - IIT; Polytechnic University of Milan
摘要：We investigate the modeling and the numerical solution of machine learning problems with prediction functions which are linear combinations of elements of a possibly infinite dictionary of functions. We propose a novel flexible composite regularization model, which makes it possible to incorporate various priors on the coefficients of the prediction function, including sparsity and hard constraints. We show that the estimators obtained by minimizing the regularized empirical risk are consisten...
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作者：Cozad, Alison; Sahinidis, Nikolaos V.
作者单位：Carnegie Mellon University; Exxon Mobil Corporation
摘要：Symbolic regression methods generate expression trees that simultaneously define the functional form of a regression model and the regression parameter values. As a result, the regression problem can search many nonlinear functional forms using only the specification of simple mathematical operators such as addition, subtraction, multiplication, and division, among others. Currently, state-of-the-art symbolic regression methods leverage genetic algorithms and adaptive programming techniques. G...
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作者：Zhang, Chong; Minh Pham; Fu, Sheng; Liu, Yufeng
作者单位：University of Waterloo; University of Virginia; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS; University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina School of Medicine
摘要：The support vector machine (SVM) is one of the most popular classification methods in the machine learning literature. Binary SVM methods have been extensively studied, and have achieved many successes in various disciplines. However, generalization to multicategory SVM (MSVM) methods can be very challenging. Many existing methods estimate k functions for k classes with an explicit sum-to-zero constraint. It was shown recently that such a formulation can be suboptimal. Moreover, many existing ...
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作者：Fischetti, Matteo; Kahr, Michael; Leitner, Markus; Monaci, Michele; Ruthmair, Mario
作者单位：University of Padua; University of Vienna; University of Bologna
摘要：Influence maximization problems aim to identify key players in (social) networks and are typically motivated from viral marketing. In this work, we introduce and study the Generalized Least Cost Influence Problem (GLCIP) that generalizes many previously considered problem variants and allows to overcome some of their limitations. A formulation that is based on the concept of activation functions is proposed together with strengthening inequalities. Exact and heuristic solution methods are deve...
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作者：Hoai An Le Thi; Tao Pham Dinh
作者单位：Universite de Lorraine
摘要：The year 2015 marks the 30th birthday of DC (Difference of Convex functions) programming and DCA (DC Algorithms) which constitute the backbone of nonconvex programming and global optimization. In this article we offer a short survey on thirty years of developments of these theoretical and algorithmic tools. The survey is comprised of three parts. In the first part we present a brief history of the field, while in the second we summarize the state-of-the-art results and recent advances. We focu...
