Boosting Functional Regression Models with FDboost

Abstract

The R add-on package FDboost is a flexible toolbox for the estimation of functional regression models by model-based boosting. It provides the possibility to fit regression models for scalar and functional response with effects of scalar as well as functional covariates, i.e., scalar-on-function, function-on-scalar and function-on-function regression models. In addition to mean regression, quantile regression models as well as generalized additive models for location scale and shape can be fitted with FDboost. Furthermore, boosting can be used in high-dimensional data settings with more covariates than observations. We provide a hands-on tutorial on model fitting and tuning, including the visualization of results. The methods for scalar-on-function regression are illustrated with spectrometric data of fossil fuels and those for functional response regression with a data set including bioelectrical signals for emotional episodes.

Classifying individuals with and without patellofemoral pain syndrome using ground force profiles – Development of a method using functional data boosting

“…All three functional variables were demeaned as a pre-processing step, so that different predictors had equal potential to be included in the model. We used component-wise gradient boosting for model fitting [12]. The algorithm is an iterative procedure which successively adds one predictor to the model with the ability to handle functional predictors, perform variable selection, and allow for penalized estimation.…”

“…The duration of the CMJ, defined from the start of the eccentric phase to toe-off was quantified, and compared between groups with a two-sample t-test, with significance defined as P < 0.05. All analyses were performed using R version 3.5.3 , using the "FDboost" package [12], and the codes with accompanying data are included in the supplementary material.…”

“…Recent advancements in machine learning techniques have enabled the simultaneous incorporation of functional and scalar predictors into statistical models for predictive modelling. One such technique is functional data boosting (FDboost) [12], a composite technique which combines functional regression with component-wise boosting. The idea of boosting is to train a strong ensemble model by combining weaker and simpler models, with the added model trying to correct the prediction errors made by the preceding model.…”

An introduction to semiparametric function-on-scalar regression

“…However, uncertainty quantification for boosting is currently only possible using computationally expensive resampling techniques like bootstrapping (Hastie et al., 2009). The method is implemented in the package (Brockhaus, 2016). Recently, this approach has also been extended to model the variance of functional responses conditional on covariates (Brockhaus et al., 2016a), using techniques developed in the literature on generalized additive models for location, scale and shape (GAMLSS; Mayr et al., 2012).…”

Object-Oriented Software for Functional Data

“…Alternative solutions for sparse data or single points in 2D are list solutions (e.g., fdapace; Chen et al 2020) or data frame based versions containing the data in a long format (e.g., fpca; Peng and Paul 2011, fdaPDE; Lila, Sangalli, Ramsay, and Formaggia 2020 or sparseFLMM; Cederbaum 2019). Some packages also accept different formats (funcy; Yassouridis 2018; Yassouridis, Ernst, and Leisch 2018 or FDboost;Brockhaus and Ruegamer 2018). A recent development is the tidyfun package (Scheipl and Goldsmith 2018), which provides representations of functional data both in a raw data format as well as in a basis representation and is particularly suited to be used in combination with packages from the tidyverse (https://www.tidyverse.org/).…”