Generative neural networks for characteristic functions
This provides a simulation tool for researchers in statistics and machine learning dealing with complex distributions, though it appears incremental as it adapts existing neural network methods to a specific representation.
The paper tackles the problem of simulating from multivariate characteristic functions accessible only as black-boxes, using a generative neural network with a loss function based on Maximum-Mean-Discrepancy to incorporate the target function, resulting in a universal algorithm with finite sample guarantees on approximation quality.
We provide a simulation algorithm to simulate from a (multivariate) characteristic function, which is only accessible in a black-box format. The method is based on a generative neural network, whose loss function exploits a specific representation of the Maximum-Mean-Discrepancy metric to directly incorporate the targeted characteristic function. The algorithm is universal in the sense that it is independent of the dimension and that it does not require any assumptions on the given characteristic function. Furthermore, finite sample guarantees on the approximation quality in terms of the Maximum-Mean Discrepancy metric are derived. The method is illustrated in a simulation study.