Stability selection for component-wise gradient boosting in multiple dimensions

TL;DR

This paper introduces a new stability selection algorithm for component-wise gradient boosting in GAMLSS models, enabling stable covariate selection and simplified tuning in complex, multi-parameter models.

Contribution

The authors develop a noncyclical boosting algorithm that incorporates stability selection for GAMLSS, reducing tuning complexity and improving variable selection stability.

Findings

Enhanced variable selection stability demonstrated in simulations

Reduced tuning complexity from multi-dimensional to one-dimensional

Successful application to eider abundance estimation with complex data

Abstract

We present a new algorithm for boosting generalized additive models for location, scale and shape (GAMLSS) that allows to incorporate stability selection, an increasingly popular way to obtain stable sets of covariates while controlling the per-family error rate (PFER). The model is fitted repeatedly to subsampled data and variables with high selection frequencies are extracted. To apply stability selection to boosted GAMLSS, we develop a new "noncyclical" fitting algorithm that incorporates an additional selection step of the best-fitting distribution parameter in each iteration. This new algorithms has the additional advantage that optimizing the tuning parameters of boosting is reduced from a multi-dimensional to a one-dimensional problem with vastly decreased complexity. The performance of the novel algorithm is evaluated in an extensive simulation study. We apply this new algorithm to a study to estimate abundance of common eider in Massachusetts, USA, featuring excess zeros, overdispersion, non-linearity and spatio-temporal structures. Eider abundance is estimated via boosted GAMLSS, allowing both mean and overdispersion to be regressed on covariates. Stability selection is used to obtain a sparse set of stable predictors.