Abstract:

We make some observations about the equivalences between regularized estimating equations, fixedpoint problems and variational inequalities: (a) A regularized estimating equation is equivalent to a fixedpoint problem, specified via the proximal operator of the corresponding penalty. (b) A regularized estimating equation is equivalent to a (generalized) variational inequality. Both equivalences extend to any estimating equations with convex penalty functions. To solve largescale regularized estimating equations, it is worth pursuing computation by exploiting these connections. While fast computational algorithms are less developed for regularized estimating equation, there are many efficient solvers for fixedpoint problems and variational inequalities. In this regard, we apply some efficient and scalable solvers which deliver hundredfold speed improvement. These connections can lead to further research in both computational and theoretical aspects of the regularized estimating equations.
