Hazem Toutounji, Daniel Durstewitz
Department of Theoretical Neuroscience, Bernstein Center for Computational Neuroscience, Central Institute of Mental Health, Medical Faculty Mannheim, Heidelberg University, Heidelberg, Germany
Correspondence: Hazem Toutounji (firstname.lastname@example.org)
BMC Neuroscience 2017, 18(Suppl 1):O19
Neural data often consist of multiple single unit recordings in the form of spike count time series. These time series are often highly nonstationary, where statistical moments, such as firing rates, vary to potentially encode features of the experimental paradigm, like changes in external input or different task phases. Changes in the firing rates may be sudden or gradual, and their time scale and onset may reflect information regarding neural computations, such as learning  or the accumulation of sensory evidence .
Here we develop an approach for detecting and parametrising multiple changes in multivariate spike count data within the statistical framework of State Space Models (SSM) . The model assumes a nonlinear, nonstationary, autoregressive Gaussian process that captures the underlying latent neural dynamics. However, given their discrete, nonnegative nature, assumptions of normality are not guaranteed to produce consistent estimates of spike count statistical moments. Instead, the Gaussian process generates spike counts by a Poisson observation function. Both latent trajectories in phase space and latent model parameters, in addition to observation model parameters, are estimated by a 3-stage Expectation-Maximisation (EM) procedure . The latter relies on Newton’s method  to maximise, under constraints, a global Laplace approximation  of spike-count data’s log-likelihood, given the SSM and its parameters. The dimensionality of the latent model equals the number of unknown nonstationary events, termed change points, and is selected by a cross-validation procedure. Observations, on the other hand, are generally of a much higher dimension than the latent dynamics. Due to this substantial dimensionality reduction , latent trajectories, thus, offer a parsimonious representation of the most relevant features in neural dynamics.
The estimation procedure is first tested on simulated data, to assure that the latent states and model parameters are correctly identified in comparison to the ground truth. As a real data example, the model is fitted to multiple single unit recordings from rat medial prefrontal cortex neurons during an operant rule switching task. The resulting reconstruction of the underlying dynamics will allow matching the neural correlates of learning to their behavioral counterpart, by relating behavioral changes to population-wide change points, as estimated by the model.
The work was funded by the German Research Foundation (DFG) (SPP1665 / DU 354/8-1) and through the German Ministry for Education and Research (BMBF) via the e:Med framework (01ZX1314E). The authors thank Dr. Florian Bähner for providing the prefrontal cortex data.
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