Deselection of base-learners for statistical boosting-with an application to distributional regression

Prediction-based variable selection for component-wise gradient boosting

Model-based component-wise gradient boosting is a popular tool for data-driven variable selection. In order to improve its prediction and selection qualities even further, several modifications of the original algorithm have been developed, that mainly focus on different stopping criteria, leaving the actual variable selection mechanism untouched. We investigate different prediction-based mechanisms for the variable selection step in model-based component-wise gradient boosting. These approaches include Akaikes Information Criterion (AIC) as well as a selection rule relying on the component-wise test error computed via cross-validation. We implemented the AIC and cross-validation routines for Generalized Linear Models and evaluated them regarding their variable selection properties and predictive performance. An extensive simulation study revealed improved selection properties whereas the prediction error could be lowered in a real world application with age-standardized COVID-19 incidence rates.

Boosting distributional copula regression

Capturing complex dependence structures between outcome variables (e.g., study endpoints) is of high relevance in contemporary biomedical data problems and medical research. Distributional copula regression provides a flexible tool to model the joint distribution of multiple outcome variables by disentangling the marginal response distributions and their dependence structure. In a regression setup, each parameter of the copula model, that is, the marginal distribution parameters and the copula dependence parameters, can be related to covariates via structured additive predictors. We propose a framework to fit distributional copula regression via model-based boosting, which is a modern estimation technique that incorporates useful features like an intrinsic variable selection mechanism, parameter shrinkage and the capability to fit regression models in high-dimensional data setting, that is, situations with more covariates than observations. Thus, model-based boosting does not only complement existing Bayesian and maximum-likelihood based estimation frameworks for this model class but rather enables unique intrinsic mechanisms that can be helpful in many applied problems. The performance of our boosting algorithm for copula regression models with continuous margins is evaluated in simulation studies that cover low- and high-dimensional data settings and situations with and without dependence between the responses. Moreover, distributional copula boosting is used to jointly analyze and predict the length and the weight of newborns conditional on sonographic measurements of the fetus before delivery together with other clinical variables.

A statistical boosting framework for polygenic risk scores based on large-scale genotype data

Polygenic risk scores (PRS) evaluate the individual genetic liability to a certain trait and are expected to play an increasingly important role in clinical risk stratification. Most often, PRS are estimated based on summary statistics of univariate effects derived from genome-wide association studies. To improve the predictive performance of PRS, it is desirable to fit multivariable models directly on the genetic data. Due to the large and high-dimensional data, a direct application of existing methods is often not feasible and new efficient algorithms are required to overcome the computational burden regarding efficiency and memory demands. We develop an adapted component-wise L 2-boosting algorithm to fit genotype data from large cohort studies to continuous outcomes using linear base-learners for the genetic variants. Similar to the snpnet approach implementing lasso regression, the proposed snpboost approach iteratively works on smaller batches of variants. By restricting the set of possible base-learners in each boosting step to variants most correlated with the residuals from previous iterations, the computational efficiency can be substantially increased without losing prediction accuracy. Furthermore, for large-scale data based on various traits from the UK Biobank we show that our method yields competitive prediction accuracy and computational efficiency compared to the snpnet approach and further commonly used methods. Due to the modular structure of boosting, our framework can be further extended to construct PRS for different outcome data and effect types-we illustrate this for the prediction of binary traits.