  High-dimensional linear and nonlinear models have been extensively used to
identify associations between response and explanatory variables. The variable
selection problem is commonly of interest in the presence of massive and
complex data. An empirical Bayes model for high-dimensional generalized linear
models (GLMs) is considered in this paper. The extension of the Iterated
Conditional Modes/Medians (ICM/M) algorithm is proposed to build up a GLM. With
the construction of pseudodata and pseudovariances based on iteratively
reweighted least squares (IRLS), conditional modes are employed to obtain
data-drive optimal values for hyperparameters and conditional medians are used
to estimate regression coefficients. With a spike-and-slab prior for each
coefficient, a conditional median can enforce variable estimation and selection
at the same time. The ICM/M algorithm can also incorporate more complicated
prior by taking the network structural information into account through the
Ising model prior. Here we focus on two extensively used models for genomic
data: binary logistic and Cox's proportional hazards models. The performance of
the proposed method is demonstrated through both simulation studies and real
data examples. The implementation of the ICM/M algorithm for both linear and
nonlinear models can be found in the icmm R package which is freely available
on CRAN.
