# A Differentiable Partially Observable Generalized Linear Model with Forward-Backward Message Passing

arXiv: https://arxiv.org/abs/2402.01263 · HTML: https://mlsanity.com/paper/2402.01263/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 24 references that are in the map.
- First posted on arXiv 2 Feb 2024.

## Builds on (most cited first, 10 of 10)

- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Gradient Estimation Using Stochastic Computation Graphs](https://mlsanity.com/paper/1506.05254/) (2015)
- [Imputing Missing Events in Continuous-Time Event Streams](https://mlsanity.com/paper/1905.05570/) (2019)
- [Bayesian latent structure discovery from multi-neuron recordings](https://mlsanity.com/paper/1610.08465/) (2016)
- [PoPPy: A Point Process Toolbox Based on PyTorch](https://mlsanity.com/paper/1810.10122/) (2018)
- [A Differentiable Point Process with Its Application to Spiking Neural Networks](https://mlsanity.com/paper/2106.00901/) (2021)
- [Forward chi2 Divergence Based Variational Importance Sampling](https://mlsanity.com/paper/2311.02516/) (2023)
- [One-hot Generalized Linear Model for Switching Brain State Discovery](https://mlsanity.com/paper/2310.15263/) (2023)

## Built on by (most cited first, 3 of 3)

- [Exploring Behavior-Relevant and Disentangled Neural Dynamics with Generative Diffusion Models](https://mlsanity.com/paper/2410.09614/) (2024)
- [Learning Time-Varying Multi-Region Brain Communications via Scalable Markovian Gaussian Processes](https://mlsanity.com/paper/2407.00397/) (2024)
- [A hitchhiker's guide to Poisson gradient estimation](https://mlsanity.com/paper/2602.03896/) (2026)

## Abstract (arXiv)

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.