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.

翻译：我们提出了一种新的计算框架，用于估计广义广义线性模型（GGLM）中的参数。GGLM是经典广义线性模型（GLM）的扩展，旨在处理时空数据中观测值之间的依赖性。该框架采用基于单调算子的变分不等式方法，克服了参数估计中的非凸性，并提供了参数恢复的保证。所得结果可应用于GLM和GGLM，尤其聚焦于时空模型。我们还利用鞅浓度不等式推导了在线基于实例的界。最后，通过数值模拟和野火事件真实数据示例展示了算法的性能。