Improved inference of latent neural states from calcium imaging data

Calcium imaging (CI) is a standard method for recording neural population activity, as it enables simultaneous recording of hundreds-to-thousands of individual somatic signals. Accordingly, CI recordings are prime candidates for population-level latent variable analyses, for example using models such as Gaussian Process Factor Analysis (GPFA), hidden Markov models (HMMs), and latent dynamical systems. However, these models have been primarily developed and fine-tuned for electrophysiological measurements of spiking activity. To adapt these models for use with the calcium signals recorded with CI, per-neuron fluorescence time-traces are typically either de-convolved to approximate spiking events or analyzed directly under Gaussian observation assumptions. The former approach, while enabling the direct application of latent variable methods developed for spiking data, suffers from the imprecise nature of spike estimation from CI. Moreover, isolated spikes can be undetectable in the fluorescence signal, creating additional uncertainty. A more direct model linking observed fluorescence to latent variables would account for these sources of uncertainty. Here, we develop accurate and tractable models for characterizing the latent structure of neural population activity from CI data. We propose to augment HMM, GPFA, and dynamical systems models with a CI observation model that consists of latent Poisson spiking and autoregressive calcium dynamics. Importantly, this model is both more flexible and directly compatible with standard methods for fitting latent models of neural dynamics. We demonstrate that using this more accurate CI observation model improves latent variable inference and model fitting on both CI observatons generated using state-of-the-art biophysical simulations as well as imaging data recorded in an experimental setting. We expect the developed methods to be widely applicable to many different analysis of population CI data.