Latent Gaussian process (GP) models are widely used in neuroscience to uncover hidden state evolutions from sequential observations, mainly in neural activity recordings. While latent GP models provide a principled and powerful solution in theory, the intractable posterior in non-conjugate settings necessitates approximate inference schemes, which may lack scalability. In this work, we propose cvHM, a general inference framework for latent GP models leveraging Hida-Mat\'ern kernels and conjugate computation variational inference (CVI). With cvHM, we are able to perform variational inference of latent neural trajectories with linear time complexity for arbitrary likelihoods. The reparameterization of stationary kernels using Hida-Mat\'ern GPs helps us connect the latent variable models that encode prior assumptions through dynamical systems to those that encode trajectory assumptions through GPs. In contrast to previous work, we use bidirectional information filtering, leading to a more concise implementation. Furthermore, we employ the Whittle approximate likelihood to achieve highly efficient hyperparameter learning.

翻译：隐高斯过程（GP）模型在神经科学中被广泛用于从顺序观测数据（主要是神经活动记录）中揭示隐藏状态演化。尽管隐高斯过程模型在理论上提供了严谨且强大的解决方案，但非共轭设置下的难解后验概率迫使研究者采用近似推断方案，这些方案往往缺乏可扩展性。本文提出cvHM，一个基于Hida-Matérn核与共轭计算变分推断（CVI）的隐GP通用推断框架。通过cvHM，我们能够对任意似然函数实现具有线性时间复杂度的隐神经轨迹变分推断。利用Hida-Matérn GP对平稳核进行重参数化，有助于将基于动力系统编码先验假设的潜变量模型与通过GP编码轨迹假设的模型相关联。与既往工作不同，我们采用双向信息滤波，使得实现更为简洁。此外，我们运用Whittle近似似然实现超参数的高效学习。