Generalized generalized linear models: Convex estimation and online bounds
Methodology
2023-04-28 v1 Machine Learning
Statistics Theory
Machine Learning
Statistics Theory
Abstract
We introduce a new computational framework for estimating parameters in generalized generalized linear models (GGLM), a class of models that extends the popular generalized linear models (GLM) to account for dependencies among observations in spatio-temporal data. The proposed approach uses a monotone operator-based variational inequality method to overcome non-convexity in parameter estimation and provide guarantees for parameter recovery. The results can be applied to GLM and GGLM, focusing on spatio-temporal models. We also present online instance-based bounds using martingale concentrations inequalities. Finally, we demonstrate the performance of the algorithm using numerical simulations and a real data example for wildfire incidents.
Keywords
Cite
@article{arxiv.2304.13793,
title = {Generalized generalized linear models: Convex estimation and online bounds},
author = {Anatoli Juditsky and Arkadi Nemirovski and Yao Xie and Chen Xu},
journal= {arXiv preprint arXiv:2304.13793},
year = {2023}
}