Primal-Dual Instrumental Variable Estimators

This paper gives a primal-dual derivation of the Least Squares Support Vector Machine (LS-SVM) using Instrumental Variables (IVs), denoted simply as the Primal-dual Instrumental Variable Estimator. Then we propose a convex optimization approach for learning the optimal instruments. Besides the traditional argumentation for the use of IVs, the primal-dual derivation gives an interesting other advantage, namely that the complexity of the system to be solved is expressed in the number of instruments, rather than in the number of samples as typically the case for SVM and LS-SVM formulations. This note explores some exciting issues in the design and analysis of such estimator.