scholarly journals Gradient boosting for linear mixed models

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Colin Griesbach ◽  
Benjamin Säfken ◽  
Elisabeth Waldmann
Keyword(s):  
Random Effects ◽  
Mixed Models ◽  
Selection Procedure ◽  
Classification Theory ◽  
Gradient Boosting ◽  
Random Structure ◽  
Boosting Algorithm ◽  
The One ◽  
Biased Estimates ◽  
Selection Of

Abstract Gradient boosting from the field of statistical learning is widely known as a powerful framework for estimation and selection of predictor effects in various regression models by adapting concepts from classification theory. Current boosting approaches also offer methods accounting for random effects and thus enable prediction of mixed models for longitudinal and clustered data. However, these approaches include several flaws resulting in unbalanced effect selection with falsely induced shrinkage and a low convergence rate on the one hand and biased estimates of the random effects on the other hand. We therefore propose a new boosting algorithm which explicitly accounts for the random structure by excluding it from the selection procedure, properly correcting the random effects estimates and in addition providing likelihood-based estimation of the random effects variance structure. The new algorithm offers an organic and unbiased fitting approach, which is shown via simulations and data examples.

Examples in the classification theory of Riemannian manifolds and the equation?u=Pu

1971 ◽  
Vol 121 (3) ◽  
pp. 233-238
Author(s):  
Moses Glasner ◽  
Richard Katz ◽  
Mitsuru Nakai
Keyword(s):  
Riemannian Manifolds ◽  
Classification Theory

New Classification Theory for Topological Gapless Superconducting Nodes

2021 ◽  
Vol 1 ◽  
Keyword(s):  
Angular Momentum ◽  
Crystal Symmetry ◽  
Classification Theory ◽  
Superconducting Gap ◽  
New Classification

A new classification theory on topological superconducting gap nodes predicts two new gap structures emerging from a nonsymmorphic crystal symmetry and angular momentum.

A STATISTICAL-FUZZY PERCEPTRON

1999 ◽  
Vol 13 (01) ◽  
pp. 33-41 ◽  
Author(s):  
M. ANDRECUT
Keyword(s):  
Classification Theory ◽  
Perceptron Algorithm ◽  
Optimal Classification ◽  
Training Sets

An optimal statistical perceptron algorithm is derived using the Bayes classification theory. The described algorithm is able to construct an optimal classification hyperplane for separable and nonseparable classes. The described algorithm can be easily improved by imposing a simple fuzzyfication scheme of the training sets.

scholarly journals On the constructions of Tits and Faulkner: an isomorphism theorem

2001 ◽  
Vol 28 (11) ◽  
pp. 673-678
Author(s):  
Sudhir R. Nath
Keyword(s):  
Jordan Algebra ◽  
Classification Theory ◽  
Closed Field ◽  
Isomorphism Theorem ◽  
Algebraically Closed Field ◽  
Split Octonions

Classification theory guarantees the existence of an isomorphism between any twoE8's, at least over an algebraically closed field of characteristic0. The purpose of this paper is to construct for any Jordan algebraJof degree3over a fieldΦof characteristic≠2,3an explicit isomorphism between the algebra obtained fromJby Faulkner's construction and the algebra obtained from the split octonions andJby Tits construction.

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