Schematic for the calcium LVMs.

A low-dimensional latent variable maps to Poisson firing rates for time-series neural population activity. These Poisson spike probabilities are marginalized over and fed through an auto-regressive process to describe the evolution of the calcium traces.

Simulated calcium HMM.

(a) Schematic for the overall calcium-HMM model. (b) The simulated data and (c) the inferred and true discrete states of the underlying latent states using different calcium models. (d) the inferred test log-likeilhoods as we vary the number of discrete latent states for different models. (e) true neural rates for each state of the underlying data alongside the inferred AR parameter mean (middle) and expected calcium fluorescence value (right).

HMM comparison on odor response data.

The calcium HMM identifies an odor onset state that is more tightly coupled with the actual odor onset.(a) Example ΔF /F traces for the population of recorded neurons on one trial. (b) Test log likelihoods for calcium and Gaussian HMMs as a function of the number of discrete states. Arrows indicate the number of discrete states with the highest test log likelihood. (c) Inferred most likely states on both training and test trials for each model. Each model identifies a consistent “odor onset” state linked to the time of odor presentation at 10s. (d) The fraction of trials in the odor onset state at each time point for each model. The calcium HMM odor onset state peaks more closely to the odor presentation window and has a shorter width (black arrows denote calculation of width).

Calcium GPFA simulated experiment using biophysical calcium imaging simulator.

(a) Graphical depiction of the biophysical calcium imaging simulator. (b) The Calcium GPFA model. (c) The temporal evolution of the three true underlying latent variables and the inferred latents from the population data using different observation likelihoods (left) and the overall estimation error of the latent variables under each model (right).

(a) Calcium LFADS model. (b) Generated latents variables as well as Poisson firing rates, spiking activity, and observed calcium traces. (c) inferred latent dynamics under an (AR1) calcium model and Gaussian likelihood. (c) latent state prediction peroformance as well as inferred and true calcium trace hyperparameters.