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 |

**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...

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
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