2016/11/03 by Frank Dondelinger, Dondelinger, Frank, Sach Mukherjee +2 · 1 citation
Computer Science · Engineering · Mathematics · #Applications (stat.AP) #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Machine Learning (stat.ML) #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1611.00953
openalex publication_date 2016/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider high-dimensional regression over subgroups of observations. Our work is motivated by biomedical problems, where disease subtypes, for example, may differ with respect to underlying regression models, but sample sizes at the subgroup-level may be limited. We focus on the case in which subgroup-specific models may be expected to be similar but not necessarily identical. Our approach is to treat subgroups as related problem instances and jointly estimate subgroup-specific regression coefficients. This is done in a penalized framework, combining an ℓ1 term with an additional term that penalizes differences between subgroup-specific coefficients. This gives solutions that are globally sparse but that allow information-sharing between the subgroups. We present algorithms for estimation and empirical results on simulated data and using Alzheimer's disease, amyotrophic lateral sclerosis and cancer datasets. These examples demonstrate the gains our approach can offer in terms of prediction and the ability to estimate subgroup-specific sparsity patterns.