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A distribution-free mixed-integer optimization approach to hierarchical modelling of clustered and longitudinal data
March 27, 2024, 4:45 a.m. | Madhav Sankaranarayanan, Intekhab Hossain, Tom Chen
stat.ML updates on arXiv.org arxiv.org
Abstract: Recent advancements in Mixed Integer Optimization (MIO) algorithms, paired with hardware enhancements, have led to significant speedups in resolving MIO problems. These strategies have been utilized for optimal subset selection, specifically for choosing $k$ features out of $p$ in linear regression given $n$ observations. In this paper, we broaden this method to facilitate cluster-aware regression, where selection aims to choose $\lambda$ out of $K$ clusters in a linear mixed effects (LMM) model with $n_k$ observations …
abstract algorithms arxiv data distribution features free hardware hierarchical linear linear regression math.oc mixed modelling optimization regression stat.me stat.ml strategies type
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