GeDS-package: GeDS

In alattuada/GeDS: Geometrically Designed Spline Regression

GeDS

Description

Geometrically Designed Splines (GeDS) regression is a non-parametric method inspired by geometric principles, which is designed for fitting spline predictor models with variable knots. This method falls within the domain of generalized non-linear models (GNM), which include generalized linear models (GLM) as a special case. GeDS regression is fitted based on a sample of N observations of a response variable y, dependent on a set of (currently up to two) covariates, assuming y has a distribution from the exponential family. In addition, GeDS methodology is implemented both in the context of Generalized Additive Models (GAM) and Functional Gradient Boosting (FGB). On the one hand, GAM consist of an additive modeling technique where the impact of the predictor variables is captured through smooth (GeDS, in this case) functions. On the other hand, GeDS incorporates gradient boosting machine learning technique by implementing functional gradient descent algorithm to optimize general risk functions utilizing component-wise GeDS estimates.

Details

The GeDS estimation method is based on: first constructing a piecewise linear fit (spline fit of order 2) at stage A which captures the shape of the data and; second approximating this fit with shape preserving (variation diminishing) spline fits of higher orders 3, 4,\dots (i.e., degrees 2, 3,\dots) at stage B. As a result of this, GeDS estimates the number and location of the knots and the order of the spline fit in a fast and efficient way.

The GeDS method was originally developed by Kaishev et al. (2016) assuming the response variable y to be normally distributed and a corresponding Mathematica code was provided.

The GeDS method was extended by Dimitrova et al. (2023) to cover any distribution from the exponential family. The GeDS R package presented here includes an enhanced R implementation of the original Normal GeDS Mathematica code due to Kaishev et al. (2016), implemented as the NGeDS function and a generalization of it in the function GGeDS which covers the case of any distribution from the exponential family.

The GeDS package allows also to fit two dimensional response surfaces and to construct multivariate (predictor) models with a GeD spline component and a parametric component (see the functions f, formula, NGeDS and GGeDS for details).

Dimitrova et al. (2024) have recently made significant enhancements to the GeDS methodology, to incorporate generalized additive models (GAM) and functional gradient boosting (FGB). On the one hand, generalized additive models are encompassed by implementing the local-scoring algorithm using normal GeD splines (i.e., NGeDS) as function smoothers within the backfitting iterations. This is implemented via the function NGeDSgam. On the other hand, the GeDS package incorporates the functional gradient descent algorithm by utilizing normal GeD splines (i.e., NGeDS) as base learners. This is implemented via the function NGeDSboost.

The outputs of both NGeDS and GGeDS functions are GeDS-class objects, while the outputs of NGeDSgam and NGeDSboost are GeDSgam-class and GeDSboost-class objects, respectively. As described in Kaishev et al. (2016), Dimitrova et al. (2023) and Dimitrova et al. (2024), the final GeDS fit is the one whose order is chosen according to a strategy described in stage B of the algorithm. However, GeDS-class, GeDSgam-class and GeDSboost-class objects contain second, third and fourth order spline fits and the user has the possibility to choose among them.

The GeDS package also includes some datasets where GeDS regression proves to be very efficient and some user friendly functions that are designed to easily extract required information. Several methods are also provided to handle GeDS, GAM-GeDS and FGB-GeDS output results (see GeDS-class, GeDSgam-class and GeDSboost-class, respectively).

Throughout this document, we use the terms GeDS predictor model, GeDS regression and GeDS fit interchangeably.

Please report any issue arising or bug in the code to [e-mail].

Package:	GeDS
Version:	0.2.0
Date:	2024-01-28
License:	GPL-3

Author(s)

Dimitrina S. Dimitrova <[e-mail]>, Emilio S. Guillen <[e-mail]>, Vladimir K. Kaishev <[e-mail]>, Andrea Lattuada <[e-mail]> and Richard J. Verrall <[e-mail]>

References

Kaishev, V.K., Dimitrova, D.S., Haberman, S., & Verrall, R.J. (2016). Geometrically designed, variable knot regression splines. Computational Statistics, 31, 1079–1105.
DOI: \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s00180-015-0621-7")}

Dimitrova, D. S., Kaishev, V. K., Lattuada, A. and Verrall, R. J. (2023). Geometrically designed variable knot splines in generalized (non-)linear models. Applied Mathematics and Computation, 436.
DOI: \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.amc.2022.127493")}

Dimitrova, D. S., Guillen, E. S. and Kaishev, V. K. (2024). GeDS: An R Package for Regression, Generalized Additive Models and Functional Gradient Boosting, based on Geometrically Designed (GeD) Splines. Manuscript submitted for publication.

See Also

Useful links:

• https://github.com/emilioluissaenzguillen/GeDS

• Report bugs at https://github.com/emilioluissaenzguillen/GeDS/issues

alattuada/GeDS documentation built on April 26, 2024, 11:36 a.m.