Z-Transforms and its Inference on Partially Observable Point Processes

This paper proposes an inference framework based on the Z-transform for a specific class of non-homogeneous point processes. This framework gives an alternative method to maximum likelihood estimation which is omnipresent in the field of point processes. The inference strategy is to couple or match the theoretical Z-transform with its empirical counterpart from the observed samples. This procedure fully characterizes the distribution of the point process since there exists a one-to-one mapping with the Z-transform. We illustrate how to use the methodology to estimate a point process whose intensity is driven by a general neural network.