Generalized generalized linear models: Convex estimation and online bounds
This work addresses the challenge of non-convexity in parameter estimation for spatio-temporal models, offering a computational framework with theoretical guarantees, though it appears incremental as an extension of existing GLM methods.
The authors tackled the problem of parameter estimation in generalized generalized linear models (GGLM) for spatio-temporal data by developing a convex estimation method using monotone operator-based variational inequalities, which provided guarantees for parameter recovery and was demonstrated through numerical simulations and a wildfire data example.
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.