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.

Perform a supervised data analysis on a database through a 'shiny' graphical interface. It includes methods such as linear regression, penalized regression, k-nearest neighbors, decision trees, ada boosting, extreme gradient boosting, random forest, neural networks, deep learning and support vector machines.

Compiling regression results into a publishable format, conducting post-hoc hypothesis testing, and plotting moderating effects (the effect of X on Y becomes stronger/weaker as Z increases).

Performs Random Subspace Method (RSM) for high-dimensional linear regression to obtain variable importance measures. The final model is chosen based on validation set or Generalized Information Criterion.

Implementation of the methods described in the paper with the above title: Langsrud, Ø. (2019) <doi:10.1007/s11222-018-9848-9>. The package can be used to generate synthetic or hybrid continuous microdata, and the relationship to the original data can be controlled in several ways. A function for replacing suppressed tabular cell frequencies with decimal numbers is included.