The expander functions rely on the mathematics developed for the Hessiandefiniteness invariance theorem for linear projection transformations of variables, described in authors' paper, to generate the full, highdimensional gradient and Hessian from the lowerdimensional derivative objects. This greatly relieves the computational burden of generating the regressionfunction 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 lowdimensional space of the base distribution. This is often a much easier task than its equivalent in the full, highdimensional space. Definiteness of Hessian can be useful in selecting optimization/sampling algorithms such as NewtonRaphson 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.
Package details 


Author  Alireza S. Mahani, Mansour T.A. Sharabiani 
Date of publication  20160908 07:33:43 
Maintainer  Alireza S. Mahani <[email protected]> 
License  GPL (>= 2) 
Version  0.7.2 
Package repository  View on CRAN 
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