Linear Time GPs for Inferring Latent Trajectories from Neural Spike Trains
This work addresses scalability issues in neuroscience for researchers analyzing neural spike data, though it is incremental as it builds on existing latent GP methods.
The paper tackled the problem of scaling latent Gaussian process models for inferring neural trajectories from spike trains by introducing cvHM, a framework using Hida-Matérn kernels and conjugate computation variational inference, achieving linear time complexity for variational inference with arbitrary likelihoods.
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-Matérn 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-Matérn 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.