RegressionFactory: Expander Functions for Generating Full Gradient and Hessian from Single-Slot and Multi-Slot Base Distributions

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The expander functions rely on the mathematics developed for the Hessian-definiteness invariance theorem for linear projection transformations of variables, described in authors' paper, to generate the full, high-dimensional gradient and Hessian from the lower-dimensional derivative objects. This greatly relieves the computational burden of generating the regression-function derivatives, which in turn can be fed into any optimization routine that utilizes such derivatives. The theorem guarantees that Hessian definiteness is preserved, meaning that reasoning about this property can be performed in the low-dimensional space of the base distribution. This is often a much easier task than its equivalent in the full, high-dimensional space. Definiteness of Hessian can be useful in selecting optimization/sampling algorithms such as Newton-Raphson optimization or its sampling equivalent, the Stochastic Newton Sampler. Finally, in addition to being a computational tool, the regression expansion framework is of conceptual value by offering new opportunities to generate novel regression problems.

Author
Alireza S. Mahani, Mansour T.A. Sharabiani
Date of publication
2016-09-08 07:33:43
Maintainer
Alireza S. Mahani <alireza.s.mahani@gmail.com>
License
GPL (>= 2)
Version
0.7.2

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Man pages

fbase1.binomial
Single-Parameter Base Log-likelihood Function(s) for Binomial...
fbase1.exponential
Single-Parameter Base Log-likelihood Function for Exponential...
fbase1.geometric
Single-Parameter Base Log-likelihood Function for Exponential...
fbase1.poisson
Single-Parameter Base Log-likelihood Function for Poisson GLM
fbase2.gamma.log.log
Double-Parameter Base Log-likelihood Function for Gamma GLM
fbase2.gaussian.identity.log
Double-Parameter Base Log-likelihood Function for Gaussian...
fbase2.inverse.gaussian.log.log
Double-Parameter Base Log-likelihood Function for...
regfac.expand.1par
Expander Function for Single-Parameter Base Distributions
regfac.expand.2par
Expander Function for Two-Parameter Base Distributions
regfac.merge
Utility Function for Adding Two Functions and Their...

Files in this package

RegressionFactory
RegressionFactory/inst
RegressionFactory/inst/doc
RegressionFactory/inst/doc/RegressionFactory.R
RegressionFactory/inst/doc/RegressionFactory.pdf
RegressionFactory/inst/doc/RegressionFactory.Rnw
RegressionFactory/NAMESPACE
RegressionFactory/R
RegressionFactory/R/utils.R
RegressionFactory/R/aaa.R
RegressionFactory/R/fbase.1par.R
RegressionFactory/R/fbase.2par.R
RegressionFactory/R/expanders.R
RegressionFactory/vignettes
RegressionFactory/vignettes/regfac_flow_diagram.pdf
RegressionFactory/vignettes/RegressionFactory.bib
RegressionFactory/vignettes/RegressionFactory.Rnw
RegressionFactory/MD5
RegressionFactory/build
RegressionFactory/build/vignette.rds
RegressionFactory/DESCRIPTION
RegressionFactory/ChangeLog
RegressionFactory/man
RegressionFactory/man/regfac.merge.Rd
RegressionFactory/man/fbase2.inverse.gaussian.log.log.Rd
RegressionFactory/man/fbase1.binomial.Rd
RegressionFactory/man/regfac.expand.1par.Rd
RegressionFactory/man/fbase1.exponential.Rd
RegressionFactory/man/regfac.expand.2par.Rd
RegressionFactory/man/fbase2.gaussian.identity.log.Rd
RegressionFactory/man/fbase2.gamma.log.log.Rd
RegressionFactory/man/fbase1.geometric.Rd
RegressionFactory/man/fbase1.poisson.Rd