A generalized EMS algorithm for model selection with incomplete data

TL;DR

This paper introduces a simplified and computationally feasible generalized EMS (GEMS) algorithm for model selection with incomplete data, applicable to high-dimensional settings, and demonstrates its effectiveness through theoretical convergence results, simulations, and real data applications.

Contribution

It proposes a new GEMS algorithm that simplifies the original EMS method, making it practical for high-dimensional data and providing convergence guarantees.

Findings

GEMS algorithm converges under mild conditions.

GEMS outperforms existing methods in simulations.

Effective in real data applications.

Abstract

Recently, a so-called E-MS algorithm was developed for model selection in the presence of missing data. Specifically, it performs the Expectation step (E step) and Model Selection step (MS step) alternately to find the minimum point of the observed generalized information criteria (GIC). In practice, it could be numerically infeasible to perform the MS-step for high dimensional settings. In this paper, we propose a more simple and feasible generalized EMS (GEMS) algorithm which simply requires a decrease in the observed GIC in the MS-step and includes the original EMS algorithm as a special case. We obtain several numerical convergence results of the GEMS algorithm under mild conditions. We apply the proposed GEMS algorithm to Gaussian graphical model selection and variable selection in generalized linear models and compare it with existing competitors via numerical experiments. We illustrate its application with three real data sets.