Learning to Simulate Sequentially Generated Data via Neural Networks and Wasserstein Training

We propose a new framework of a neural network-assisted sequential structured simulator to model, estimate, and simulate a wide class of sequentially generated data. Neural networks are integrated into the sequentially structured simulators in order to capture potential nonlinear and complicated sequential structures. Given representative real data, the neural network parameters in the simulator are estimated and calibrated through a Wasserstein training process, without restrictive distributional assumptions. The target of Wasserstein training is to enforce the joint distribution of the simulated data to match the joint distribution of the real data in terms of Wasserstein distance. Moreover, the neural network-assisted sequential structured simulator can flexibly incorporate various kinds of elementary randomness and generate distributions with certain properties such as heavy-tail, without the need to redesign the estimation and training procedures. Further, regarding statistical properties, we provide results on consistency and convergence rate for the estimation procedure of the proposed simulator, which are the first set of results that allow the training data samples to be correlated. We then present numerical experiments with synthetic and real data sets to illustrate the performance of the proposed simulator and estimation procedure.