Estimating latent neuronal nonlinear dynamics by sequential Monte Carlo method and sparse modeling.

Understanding complex neuronal behavior in our brain requires accurate estimation of neuronal models from observed time-series data. In this study, we propose a data-driven sparse modeling method to estimate multi-dimensional latent variables and electrical properties while extracting essential membrane currents from partially observable time series data. First, we derive a nonlinear state space model from a conductance-based neuron model that couples membrane potential and calcium concentration including a set of candidate membrane currents. Then, we derive a sparse modeling-based expectation-maximization (EM) algorithm. In the expectation step, the expectation of the log-likelihood with Laplace prior distribution is evaluated using the posterior distribution of latent states, which is approximated by a sequential Monte Carlo (SMC) method under one-dimensional noisy observations. In the maximization step, the conductances are estimated as zero value for unnecessary currents whereas those are estimated as non-zero value for necessary currents. We show using simulation with conductance-based neuron model that the proposed method can extract the latent nonlinear neuronal dynamics from partially observable data by estimating latent variables and biophysical parameters and extracting only necessary membrane currents.