A key problem in neuroscience and life sciences more generally is that the data generation process is often best thought of as a hierarchy of dynamic systems. One example of this is in-vivo calcium imaging data, where observed calcium transients are driven by a combination of electro-chemical kinetics where hypothesized trajectories around manifolds determining the frequency of these transients. A recent approach using sequential variational auto-encoders demonstrated it was possible to learn the latent dynamic structure of reaching behaviour from spiking data modelled as a Poisson process. Here we extend this approach using a ladder method to infer the spiking events driving calcium transients along with the deeper latent dynamic system. We show strong performance of this approach on a benchmark synthetic dataset against a number of alternatives.
We propose an extension to LFADS capable of inferring spike trains to reconstruct calcium fluorescence traces using hierarchical VAEs.