Generalized generalized linear models: Convex estimation and online bounds

TL;DR

This paper introduces a new convex estimation framework for generalized generalized linear models (GGLM) that handles dependencies in spatio-temporal data, providing online bounds and demonstrating effectiveness through simulations and real wildfire data.

Contribution

It develops a monotone operator-based variational inequality method for convex parameter estimation in GGLMs, extending GLMs to dependent data with online bounds.

Findings

Effective parameter recovery guarantees for GGLMs.

Successful application to wildfire incident data.

Numerical simulations validate the proposed method.

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.