Using the theory of random point processes, a method is presented whereby functional relationships between neurons can be detected and modeled. The method is based on a point process characterization involving stochastic intensities and an additive rate function model. Estimates are based on the maximum likelihood (ML) principle and asymptotic properties are examined in the absence of a stationarity assumption. An iterative algorithm that computes the ML estimates is presented. It is based on the expectation/maximization (EM) procedure of Dempster et al. (1977) and makes ML identification accessible to models requiring many parameters. Examples illustrating the use of the method are also presented. These examples are derived from simulations of simple neural systems that cannot be identified using correlation techniques. It is shown that the ML method correctly identifies each of these systems.

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Diffusion models have seen tremendous success as generative architectures. Recently, they have been shown to be effective at modelling policies for offline reinforcement learning and imitation learning. We explore using diffusion as a model class for the successor state measure (SSM) of a policy. We find that enforcing the Bellman flow constraints leads to a simple Bellman update on the diffusion step distribution.

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