Common-input models for multiple neural spike-train data

Recent developments in multi-electrode recordings enable the simultaneous measurement of the spiking activity of many neurons. Analysis of such multineuronal data is one of the key challenge in computational neuroscience today. In this work, we develop a multivariate point-process model in which the observed activity of a network of neurons depends on three terms: (1) the experimentally-controlled stimulus; (2) the spiking history of the observed neurons; and (3) a hidden term that corresponds, for example, to common input from an unobserved population of neurons that is presynaptic to two or more cells in the observed population. We consider two models for the network firing-rates, one of which is computationally and analytically tractable but can lead to unrealistically high firing-rates, while the other with reasonable firing-rates imposes a greater computational burden. We develop an expectation-maximization algorithm for fitting the parameters of both the models. For the analytically tractable model the expectation step is based on a continuous-time implementation of the extended Kalman smoother, and the maximization step involves two concave maximization problems which may be solved in parallel. The other model that we consider necessitates the use of Monte Carlo methods for the expectation as well as maximization step. We discuss the trade-off involved in choosing between the two models and the associated methods. The techniques developed allow us to solve a variety of inference problems in a straightforward, computationally efficient fashion; for example, we may use the model to predict network activity given an arbitrary stimulus, infer a neuron's ring rate given the stimulus and the activity of the other observed neurons, and perform optimal stimulus decoding and prediction. We present several detailed simulation studies which explore the strengths and limitations of our approach.