  The partially observable generalized linear model (POGLM) is a powerful tool
for understanding neural connectivity under the assumption of existing hidden
neurons. With spike trains only recorded from visible neurons, existing works
use variational inference to learn POGLM meanwhile presenting the difficulty of
learning this latent variable model. There are two main issues: (1) the sampled
Poisson hidden spike count hinders the use of the pathwise gradient estimator
in VI; and (2) the existing design of the variational model is neither
expressive nor time-efficient, which further affects the performance. For (1),
we propose a new differentiable POGLM, which enables the pathwise gradient
estimator, better than the score function gradient estimator used in existing
works. For (2), we propose the forward-backward message-passing sampling scheme
for the variational model. Comprehensive experiments show that our
differentiable POGLMs with our forward-backward message passing produce a
better performance on one synthetic and two real-world datasets. Furthermore,
our new method yields more interpretable parameters, underscoring its
significance in neuroscience.
