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Non-monotonic Feature Selection for Regression
2014Feature selection is an important research problem in machine learning and data mining. It is usually constrained by the budget of the feature subset size in practical applications. When the budget changes, the ranks of features in the selected feature subsets may also change due to nonlinear cost functions for acquisition of features. This property is
Haiqin Yang +3 more
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2010
In some applications, we require a monotone estimate of a regression function. In others, we want to test whether the regression function is monotone. For solving the first problem, Ramsay's, Kelly and Rice's, as well as point-wise monotone regression functions in a spline space are discussed and their properties developed. Three monotone estimates are
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In some applications, we require a monotone estimate of a regression function. In others, we want to test whether the regression function is monotone. For solving the first problem, Ramsay's, Kelly and Rice's, as well as point-wise monotone regression functions in a spline space are discussed and their properties developed. Three monotone estimates are
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A Solution to the Problem of Monotone Likelihood in Cox Regression
Biometrics, 2001Summary.The phenomenon of monotone likelihood is observed in the fitting process of a Cox model if the likelihood converges to a finite value while at least one parameter estimate diverges to ±∞. Monotone likelihood primarily occurs in small samples with substantial censoring of survival times and several highly predictive covariates.
Heinze, Georg, Schemper, Michael
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A Boosting Approach to Generalized Monotonic Regression
2007We propose a novel approach for generalized additive regression problems, where one or more smooth components are assumed to have monotonic influence on the dependent variable. The response is allowed to follow a simple exponential family. Smooth estimates are obtained by expansion of the unknown functions into B-spline basis functions, where the ...
Florian Leitenstorfer, Gerhard Tutz 0001
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Monotone Regression: Continuity and Differentiability Properties
Psychometrika, 1971Least-squares monotone regression has received considerable discussion and use. Consider the residual sum of squares Q obtained from the least-squares monotone regression of yi on xi. Treating Q as a function of the yi, we prove that the gradient ▽Q exists and is continuous everywhere, and is given by a simple formula.
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Algorithms for Sparse k-Monotone Regression
2018The problem of constructing k-monotone regression is to find a vector \(z\in \mathbb {R}^n\) with the lowest square error of approximation to a given vector \(y\in \mathbb {R}^n\) (not necessary k-monotone) under condition of k-monotonicity of z. The problem can be rewritten in the form of a convex programming problem with linear constraints. The paper
Sergei P. Sidorov +3 more
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A Kolmogorov-type test for monotonicity of regression
Statistics & Probability Letters, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Generalized smooth monotonic regression
2005Common approaches to monotonic regression focus on the case of a unidimensional covariate and continuous dependent variable. Here a general approach is proposed that allows for additive and multiplicative structures where one or more variables have monotone influence on the dependent variable.
Tutz, Gerhard, Leitenstorfer, Florian
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