Extend AdapDISCOM to generalized linear and longitudinal models, and explore alternative penalties

Develop and assess extensions of AdapDISCOM—an adaptive direct sparse regression procedure using multimodal covariance, originally formulated for linear models under missing completely at random (MCAR)—to generalized linear models and to longitudinal data settings, and investigate alternative sparsity-inducing penalty functions beyond the standard LASSO within this framework.

Background

AdapDISCOM is proposed as an adaptive multimodal covariance-based sparse regression method that addresses simultaneous block-wise missingness and measurement error in high-dimensional linear models. The method provides theoretical guarantees, robust variants for heavy-tailed data, and a computationally efficient tuning strategy.

The authors note that, while effective for linear models, further development is needed to handle generalized linear models and longitudinal data, and to consider penalties beyond LASSO. These directions are explicitly identified as open extensions of the current framework.