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Abstract:
Neurons within cortical populations are tightly coupled into collective dynamical systems that code and compute
cooperatively. This dynamical coupling leads to firing variability which is structured across both neurons and
time, and which can be described by statistical models where a latent low-dimensional (‘state-space’) stochastic
process represents the common effect of network activity on the recorded cells. However, such state-space
models can be challenging to fit to experimental data. The discrete nature of spiking leads to non-linear and non-
Gaussian models, necessitating approximations during model estimation that may be computationally intensive
or error-prone. Furthermore, the likelihood function—the quality of fit as a function of model parameters—may
have multiple maxima, making it difficult to find the overall best model amongst many locally-optimal ones. We
present an algorithm which improves the efficiency and robustness of estimation for statistical models in which
a latent stochastic linear dynamical system (LDS) drives generalised-linear repre- sentations of individual cells.
Our algorithm is based on an engineering approach called subspace identification (SSID). SSID was developed
to estimate LDS models of Gaussian variables and works by identifying low-dimensional structure in the matrix
of covariances between anisochronic measurements. It yields a unique and statistically consistent estimate at
relatively little cost. We have extended SSID to the generalised-linear setting. The extended SSID learns a
good model of neural population activity. On large simulated data sets with Poisson spike-counts, the algorithm
recovers the correct parameters rapidly, without iter- ation or approximation. On multi-electrode cortical recordings
it provides an effective initialisation for conventional maximum-likelihood estimation, avoiding poor local optima
and substantially speed- ing convergence. Thus the new approach promises to render state-space methods with
non-Gaussian observations far more practicable.
