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

Linear Time GPs for Inferring Latent Trajectories from Neural Spike Trains