TY - JOUR

T1 - Extended differential geometric LARS for high-dimensional GLMs with general dispersion parameter

AU - Augugliaro, Luigi

AU - Pazira, Hassan

AU - Wit, Ernst

PY - 2018

Y1 - 2018

N2 - A large class of modeling and prediction problems involves outcomes that belong to an exponential family distribution. Generalized linear models (GLMs) are a standard way of dealing with such situations. Even in high-dimensional feature spaces GLMs can be extended to deal with such situations. Penalized inference approaches, such as the (Formula presented.) or SCAD, or extensions of least angle regression, such as dgLARS, have been proposed to deal with GLMs with high-dimensional feature spaces. Although the theory underlying these methods is in principle generic, the implementation has remained restricted to dispersion-free models, such as the Poisson and logistic regression models. The aim of this manuscript is to extend the differential geometric least angle regression method for high-dimensional GLMs to arbitrary exponential dispersion family distributions with arbitrary link functions. This entails, first, extending the predictorâcorrector (PC) algorithm to arbitrary distributions and link functions, and second, proposing an efficient estimator of the dispersion parameter. Furthermore, improvements to the computational algorithm lead to an important speed-up of the PC algorithm. Simulations provide supportive evidence concerning the proposed efficient algorithms for estimating coefficients and dispersion parameter. The resulting method has been implemented in our R package (which will be merged with the original dglars package) and is shown to be an effective method for inference for arbitrary classes of GLMs.

AB - A large class of modeling and prediction problems involves outcomes that belong to an exponential family distribution. Generalized linear models (GLMs) are a standard way of dealing with such situations. Even in high-dimensional feature spaces GLMs can be extended to deal with such situations. Penalized inference approaches, such as the (Formula presented.) or SCAD, or extensions of least angle regression, such as dgLARS, have been proposed to deal with GLMs with high-dimensional feature spaces. Although the theory underlying these methods is in principle generic, the implementation has remained restricted to dispersion-free models, such as the Poisson and logistic regression models. The aim of this manuscript is to extend the differential geometric least angle regression method for high-dimensional GLMs to arbitrary exponential dispersion family distributions with arbitrary link functions. This entails, first, extending the predictorâcorrector (PC) algorithm to arbitrary distributions and link functions, and second, proposing an efficient estimator of the dispersion parameter. Furthermore, improvements to the computational algorithm lead to an important speed-up of the PC algorithm. Simulations provide supportive evidence concerning the proposed efficient algorithms for estimating coefficients and dispersion parameter. The resulting method has been implemented in our R package (which will be merged with the original dglars package) and is shown to be an effective method for inference for arbitrary classes of GLMs.

KW - Dispersion paremeter; Generalized linear models; High-dimensional inference; Least angle regression; Predictor-corrector algorithm; Theoretical Computer Science; Statistics and Probability; Statistics

KW - Probability and Uncertainty; Computational Theory and Mathematics

KW - Dispersion paremeter; Generalized linear models; High-dimensional inference; Least angle regression; Predictor-corrector algorithm; Theoretical Computer Science; Statistics and Probability; Statistics

KW - Probability and Uncertainty; Computational Theory and Mathematics

UR - http://hdl.handle.net/10447/244493

UR - https://link.springer.com/article/10.1007/s11222-017-9761-7

M3 - Article

VL - 28

SP - 753

EP - 774

JO - Statistics and Computing

JF - Statistics and Computing

SN - 0960-3174

ER -