## Common-input models for multiple neural spike-train data

Network: Computation in Neural Systems, Volume 18, 2007,
pages 375-407.

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.

Reprint | Related work on likelihood-based spike train
modeling | Liam
Paninski's research page