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.

翻译：部分可观测广义线性模型（POGLM）是在存在隐藏神经元假设下理解神经连接性的有力工具。由于仅能从可见神经元记录尖峰序列，现有研究采用变分推断学习POGLM，但同时也暴露了学习该隐变量模型的困难。主要存在两个问题：（1）采样的泊松隐藏尖峰计数阻碍了变分推断中路径梯度估计器的使用；（2）现有变分模型的设计既缺乏表达力又时间效率低下，进一步影响了性能。针对问题（1），我们提出一种新型可微分POGLM，能够使用路径梯度估计器，其性能优于现有研究中使用的分数函数梯度估计器。针对问题（2），我们提出用于变分模型的前向-后向消息传递采样方案。综合实验表明，采用我们提出的前向-后向消息传递的可微分POGLM在一个人工数据集和两个真实数据集上取得了更优性能。此外，我们的新方法能产生更具可解释性的参数，凸显了其在神经科学领域的重要意义。