Improved estimation of latent variable models from calcium imaging data

Calcium imaging (CI) has emerged as a prominent method for recording neural population activity. Therefore, CI recordings are prime candidates for the application of latent variable models designed to identify latent neural states and dynamics. However, in CI experiments spiking events are measured only indirectly via calcium ions that rapidly enter a cell during action potentials and then slowly seep back out. To analyze CI data, per-neuron fluorescence time-traces are typically either de-convolved to approximate spiking events or analyzed directly. The former approach, although enabling many methods developed for spiking data to be trivially applied to CI, can introduce errors via mis-estimation of spikes. Alternatively, direct modeling typically relies on Gaussian observation models, despite the mismatch to autoregressive calcium dynamics.

Here, we develop accurate yet tractable models for characterizing the latent structure of neural population activity directly from CI data. We augment three standard neural population models, Gaussian Process Factor Analysis (GPFA), hidden Markov Models (HMMs), and latent dynamical systems, with a CI observation model (Ganmor et al. 2016). The CI observation model has autoregressive calcium dynamics with spike count influxes driven by a latent Poisson variable, and therefore can address both of the shortcomings of deconvolution and Gaussian observation approaches. To fit the models, we develop inference methods using variational and Laplace approximations. We demonstrate that using a more accurate CI observation model improves latent variable inference and model fitting on both CI generated using state-of-the-art biophysical simulations, as well as imaging data recorded in an experimental setting. Finally, we also propose extensions to the CI observation model to account for nonlinear relationships between spiking activity and the calcium influx. We expect the developed methods to be widely applicable for analysis of CI recordings.