Gradient boosting from the field of statistical learning is widely known as a powerful framework for estimation and selection of predictor effects in various regression models by adapting concepts from classification theory. Current boosting approaches also offer methods accounting for random effects and thus enable prediction of mixed models for longitudinal and clustered data. However, these approaches include several flaws resulting in unbalanced effect selection with falsely induced shrinkage and a low convergence rate on the one hand and biased estimates of the random effects on the other hand. We therefore propose a new boosting algorithm which explicitly accounts for the random structure by excluding it from the selection procedure, properly correcting the random effects estimates and in addition providing likelihood-based estimation of the random effects variance structure. The new algorithm offers an organic and unbiased fitting approach, which is shown via simulations and data examples.
Boosting techniques from the field of statistical learning have grown to be a popular tool for estimating and selecting predictor effects in various regression models and can roughly be separated in two general approaches, namely gradient boosting and likelihood-based boosting. An extensive framework has been proposed in order to fit generalised mixed models based on boosting, however for the case of cluster-constant covariates likelihood-based boosting approaches tend to mischoose variables in the selection step leading to wrong estimates. We propose an improved boosting algorithm for linear …
Extreme quantile regression provides estimates of conditional quantiles outside the range of the data. Classical quantile regression performs poorly in such cases since data in the tail region are too scarce. Extreme value theory is used for extrapolation beyond the range of observed values and estimation of conditional extreme quantiles. Based on the peaks-over-threshold approach, the conditional distribution above a high threshold is approximated by a generalized Pareto distribution with covariate dependent parameters. We propose a gradient boosting procedure to estimate a conditional genera…
In various data situations joint models are an efficient tool to analyze relationships between time dependent covariates and event times or to correct for event-dependent dropout occurring in regression analysis. Joint modeling connects a longitudinal and a survival submodel within a single joint likelihood which then can be maximized by standard optimization methods. Main burdens of these conventional methods are that the computational effort increases rapidly in higher dimensions and they do not offer special tools for proper variable selection. Gradient boosting techniques are well known am…
Tuning of model-based boosting algorithms relies mainly on the number of iterations, while the step-length is fixed at a predefined value. For complex models with several predictors such as Generalized Additive Models for Location, Scale and Shape (GAMLSS), imbalanced updates of predictors, where some distribution parameters are updated more frequently than others, can be a problem that prevents some submodels to be appropriately fitted within a limited number of boosting iterations. We propose an approach using adaptive step-length (ASL) determination within a non-cyclical boosting algorithm …
In randomized clinical trials with survival outcome, there has been an increasing interest in subgroup identification based on baseline genomic, proteomic markers or clinical characteristics. Some of the existing methods identify subgroups that benefit substantially from the experimental treatment by directly modeling outcomes or treatment effect. When the goal is to find an optimal treatment for a given patient rather than finding the right patient for a given treatment, methods under the individualized treatment regime framework estimate an individualized treatment rule that would lead to th…
Boosting methods are widely used in statistical learning to deal with high-dimensional data due to their variable selection feature. However, those methods lack straightforward ways to construct estimators for the precision of the parameters such as variance or confidence interval, which can be achieved by conventional statistical methods like Bayesian inference. In this paper, we propose a new inference method "BayesBoost" that combines boosting and Bayesian for linear mixed models to make the uncertainty estimation for the random effects possible on the one hand. On the other hand, the new m…
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-wi…
Tweedie's compound Poisson model is a popular method to model insurance claims with probability mass at zero and nonnegative, highly right-skewed distribution. In particular, it is not uncommon to have extremely unbalanced data with excessively large proportion of zero claims, and even traditional Tweedie model may not be satisfactory for fitting the data. In this paper, we propose a boosting-assisted zero-inflated Tweedie model, called EMTboost, that allows zero probability mass to exceed a traditional model. We makes a nonparametric assumption on its Tweedie model component, that unlike a li…
An information theoretic approach to learning the complexity of classification and regression trees and the number of trees in gradient tree boosting is proposed. The optimism (test loss minus training loss) of the greedy leaf splitting procedure is shown to be the maximum of a Cox-Ingersoll-Ross process, from which a generalization-error based information criterion is formed. The proposed procedure allows fast local model selection without cross validation based hyper parameter tuning, and hence efficient and automatic comparison among the large number of models performed during each boosting…
Improving existing widely-adopted prediction models is often a more efficient and robust way towards progress than training new models from scratch. Existing models may (a) incorporate complex mechanistic knowledge, (b) leverage proprietary information and, (c) have surmounted barriers to adoption. Compared to model training, model improvement and modification receive little attention. In this paper we propose a general approach to model improvement: we combine gradient boosting with any previously developed model to improve model performance while retaining important existing characteristics.…
Statistical Inference for Gradient Boosting Regression
School of Economics, Fudan University（复旦大学经济学院）；Department of Statistics and Data Science, The Wharton School, University of Pennsylvania（宾夕法尼亚大学沃顿商学院统计与数据科学系）
We propose a novel class of flexible latent-state time series regression models which we call Markov-switching generalized additive models for location, scale and shape. In contrast to conventional Markov-switching regression models, the presented methodology allows us to model different state-dependent parameters of the response distribution - not only the mean, but also variance, skewness and kurtosis parameters - as potentially smooth functions of a given set of explanatory variables. In addition, the set of possible distributions that can be specified for the response is not limited to the…
Gradient boosting algorithms construct a regression predictor using a linear combination of ``base learners''. Boosting also offers an approach to obtaining robust non-parametric regression estimators that are scalable to applications with many explanatory variables. The robust boosting algorithm is based on a two-stage approach, similar to what is done for robust linear regression: it first minimizes a robust residual scale estimator, and then improves it by optimizing a bounded loss function. Unlike previous robust boosting proposals this approach does not require computing an ad-hoc residua…
Tax evasion is the illegal evasion of taxes by individuals, corporations, and trusts. The revenue loss from tax avoidance can undermine the effectiveness and equity of the government policies. A standard measure of tax evasion is the tax gap, that can be estimated as the difference between the total amounts of tax theoretically collectable and the total amounts of tax actually collected in a given period. This paper presents an original contribution to bottom-up approach, based on results from fiscal audits, through the use of Machine Learning. The major disadvantage of bottom-up approaches is…
