Proximal boosting and its acceleration

Gradient boosting is a prediction method that iteratively combines weak learners to produce a complex and accurate model. From an optimization point of view, the learning procedure of gradient boosting mimics a gradient descent on a functional variable. This paper proposes to build upon the proximal point algorithm when the empirical risk to minimize is not differentiable to introduce a novel boosting approach, called proximal boosting. Besides being motivated by non-differentiable optimization, the proposed algorithm benefits from Nesterov's acceleration in the same way as gradient boosting [Biau et al., 2018]. This leads to a variant, called accelerated proximal boosting. Advantages of leveraging proximal methods for boosting are illustrated by numerical experiments on simulated and real-world data. In particular, we exhibit a favorable comparison over gradient boosting regarding convergence rate and prediction accuracy

Estimation and Regularization Techniques for Regression Models with Multidimensional Prediction Functions

Boosting is one of the most important methods for fitting regression models and building prediction rules from high-dimensional data. A notable feature of boosting is that the technique has a built-in mechanism for shrinking coefficient estimates and variable selection. This regularization mechanism makes boosting a suitable method for analyzing data characterized by small sample sizes and large numbers of predictors. We extend the existing methodology by developing a boosting method for prediction functions with multiple components. Such multidimensional functions occur in many types of statistical models, for example in count data models and in models involving outcome variables with a mixture distribution. As will be demonstrated, the new algorithm is suitable for both the estimation of the prediction function and regularization of the estimates. In addition, nuisance parameters can be estimated simultaneously with the prediction function

An update on statistical boosting in biomedicine

Statistical boosting algorithms have triggered a lot of research during the last decade. They combine a powerful machine-learning approach with classical statistical modelling, offering various practical advantages like automated variable selection and implicit regularization of effect estimates. They are extremely flexible, as the underlying base-learners (regression functions defining the type of effect for the explanatory variables) can be combined with any kind of loss function (target function to be optimized, defining the type of regression setting). In this review article, we highlight the most recent methodological developments on statistical boosting regarding variable selection, functional regression and advanced time-to-event modelling. Additionally, we provide a short overview on relevant applications of statistical boosting in biomedicine

Model-based Boosting in R: A Hands-on Tutorial Using the R Package mboost

We provide a detailed hands-on tutorial for the R add-on package mboost. The package implements boosting for optimizing general risk functions utilizing component-wise (penalized) least squares estimates as base-learners for fitting various kinds of generalized linear and generalized additive models to potentially high-dimensional data. We give a theoretical background and demonstrate how mboost can be used to fit interpretable models of different complexity. As an example we use mboost to predict the body fat based on anthropometric measurements throughout the tutorial