Reverse engineering of gene regulatory networks remains a central challenge in computational systems biology, despite recent advances facilitated by benchmark in-silico challenges that have aided in calibrating their performance. A number of approaches using either perturbation (knock-out) or wild-type time series data have appeared in the literature addressing this problem, with the latter employing linear temporal models. Nonlinear dynamical models are particularly appropriate for this inference task given the generation mechanism of the time series data. In this study, we introduce a novel nonlinear autoregressive model based on operator-valued kernels that simultaneously learns the model parameters, as well as the network structure. A flexible boosting algorithm (OKVAR-Boost) that shares features from L2-boosting and randomization-based algorithms is developed to perform the tasks of parameter learning and network inference for the proposed model. Specifically, at each boosting iteration, a regularized operator-valued kernel based vector autoregressive model (OKVAR) is trained on a random subnetwork. The final model consists of an ensemble of such models. The empirical estimation of the ensemble model's Jacobian matrix provides an estimation of the network structure. The performance of the proposed algorithm is evaluated on a number of benchmark data sets from the DREAM3 challenge. The high quality results obtained strongly indicate that it outperforms existing approaches.