Time series GLM’s by convex programming
Résumé
We introduce a new computational framework for estimating parameters of generalized linear models.The proposed approach relies upon a monotone operator-based variational inequalities framework to overcome non-convexity of the loss functions of the parameter estimation problem and leads to non-asymptotic guarantees for parameter recovery.Our focus is on a class of spatio-temporal models which can be seen as alarge-scale generalization of Wiener and Hammerstein-Wiener nonlinear autoregressive models [1,2] with monotone nonlinearity,and also an extension of the popular generalized linear model(GLM)class[3] to account for dependencies among observations in spatio-temporal data. Proposed estimates are accompanied with online instance-based accuracy bounds which use observations.Such bounds rely upon new “computation-friendly counterpart” of classical concentration inequalities for martingales [4]. Finally, to illustrate the performance of the proposed estimation routines,we discuss results of a preliminary numerical study of Poisson spatio-temporal model based on simulated and real data.