Inversion-based feedforward control enables high performance for industrial motion systems. To this end, accurate knowledge of the inverse system is required, and non-causal control actions must be enabled. The aim of this paper is to accurately identify non-causal inverse models in view of high feedforward control performance. The developed method employs kernel-based regularization to minimize the mean squared error of the estimate. The performance benefits of the presented approach are demonstrated on an industrial printing system, including non-causal feedforward control actions.