Feature Screening in Ultrahigh Dimensional Generalized Varying-coefficient Models

Abstract

Generalized varying coefficient models are particularly useful for examining dynamic effects of covariates on a continuous, binary or count response. This paper is concerned with feature screening for generalized varying coefficient models with ultrahigh dimensional covariates. The proposed screening procedure is based on joint quasi-likelihood of all predictors, and therefore is distinguished from marginal screening procedures proposed in the literature. In particular, the proposed procedure can effectively identify active predictors that are jointly dependent but marginally independent of the response. In order to carry out the proposed procedure, we propose an effective algorithm and establish the ascent property of the proposed algorithm. We further prove that the proposed procedure possesses the sure screening property. That is, with probability tending to one, the selected variable set includes the actual active predictors. We examine the finite sample performance of the proposed procedure and compare it with existing ones via Monte Carlo simulations, and illustrate the proposed procedure by a real data example.

Determination of melon seed physical parameters and calibration of discrete element simulation parameters

“…In the mechanical sowing process, seeds are subject to mutual collisions and interactions with the sowing machinery. Investigating the collision recovery coefficient of seeds holds significant importance [ 21 ]. The Seed collision recovery coefficient is a fundamental granular property required for building a discrete element simulation.…”

Forward variable selection for sparse ultra-high-dimensional generalized varying coefficient models

“…We describe our simulation setups. When we generate the index variable Z ∈ [0, 1], the covariate vector X ∈ R p and the response variable Y , we follow the same spirit in the simulation settings of Yang, Yang and Li (2020). We first sample (Z * , X)…”

“…Xia, Yang and Li (2016) applied NIS to generalized varying coefficient models. Yang, Yang and Li (2020) proposed an approximated log-likelihood method as in their (2.8) for generalized varying coefficient models. The procedure can improve the log-likelihood function when their conditions on the observed high-dimensional Fisher information matrix are satisfied.…”

“…See Remark 1 at the end of 3. NUMERICAL STUDIES20 this subsection.We use both the stopping rule (2.2) and the high-dimensional BIC (HBIC) ofYang, Yang and Li (2020) to terminate the iteration of FR and SC. The HBIC criterion is included for comparison although it is not theoretically justified yet for the present setup.…”