Instrumental variable regression via kernel maximum moment loss

Abstract We investigate a simple objective for nonlinear instrumental variable (IV) regression based on kernelized conditional moment restriction known as maximum (MMR). The MMR is formulated by maximizing the interaction between residual and instruments belonging to unit ball in reproducing kernel Hilbert space. First, it allows us simplify IV an empirical risk minimization problem, where function depends instrument can be estimated U -statistic or V -statistic. Second, basis this simplification, we are able provide consistency asymptotic normality results both parametric nonparametric settings. Finally, easy-to-use algorithms with efficient hyperparameter selection procedure. demonstrate effectiveness of our using experiments synthetic real-world data.