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Consistency of Multidimensional Convex Regression
Operations Research, 2012Convex regression is concerned with computing the best fit of a convex function to a data set of n observations in which the independent variable is (possibly) multidimensional. Such regression problems arise in operations research, economics, and other disciplines in which imposing a convexity constraint on the regression function is natural.
Eunji Lim, Peter W. Glynn
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Lagrangian support vector regression via unconstrained convex minimization
Neural Networks, 2014In this paper, a simple reformulation of the Lagrangian dual of the 2-norm support vector regression (SVR) is proposed as an unconstrained minimization problem. This formulation has the advantage that its objective function is strongly convex and further having only m variables, where m is the number of input data points.
Balasundaram, S., Gupta, Deepak, Kapil
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On uniform consistent estimators for convex regression
Journal of Nonparametric Statistics, 2011A new nonparametric estimator of a convex regression function in any dimension is proposed and its uniform convergence properties are studied.
Néstor Aguilera +2 more
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INFORMS Journal on Computing, 2021
We consider the problem of best [Formula: see text]-subset convex regression using [Formula: see text] observations in [Formula: see text] variables. For the case without sparsity, we develop a scalable algorithm for obtaining high quality solutions in practical times that compare favorably with other state of the art methods.
Dimitris Bertsimas, Nishanth Mundru
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We consider the problem of best [Formula: see text]-subset convex regression using [Formula: see text] observations in [Formula: see text] variables. For the case without sparsity, we develop a scalable algorithm for obtaining high quality solutions in practical times that compare favorably with other state of the art methods.
Dimitris Bertsimas, Nishanth Mundru
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Non-convex isotonic regression via the Myersonian approach
Statistics & Probability Letters, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhenyu Cui +3 more
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Regression Models for Convex ROC Curves
Biometrics, 2000Summary. The performance of a diagnostic test is summarized by its receiver operating characteristic (ROC) curve. Under quite natural assumptions about the latent variable underlying the test, the ROC curve is convex. Empirical data on a test's performance often comes in the form of observed true positive and false positive relative frequencies under ...
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A test for linear versus convex regression function using shape-restricted regression
Biometrika, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Convex Regression: Theory, Practice, and Applications
2016This thesis explores theoretical, computational, and practical aspects of convex (shape-constrained) regression, providing new excess risk upper bounds, a comparison of convex regression techniques with theoretical guarantee, a novel heuristic training algorithm for max-affine representations, and applications in convex stochastic programming.
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High-Dimensional Structured Regression Using Convex Optimization
2018While the term "Big Data" can have multiple meanings, we consider the type of data in which the number of features can be much greater than the number of observations (also known as high-dimensional data). High-dimensional data is abundant in contemporary scientific research due to the rapid advances in new data-measurement technologies and computing ...
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Learning Convex Optimization Models
IEEE/CAA Journal of Automatica Sinica, 2021Shane Barratt, Stephen Boyd
exaly