Integral equation methods for computing likelihoods and their derivatives in the stochastic integrate-and-fire model |
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Authors: | Liam Paninski Adrian Haith Gabor Szirtes |
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Institution: | (1) Department of Statistics, Columbia University, New York, NY, USA;(2) Institute for Perception, Action and Behaviour, University of Edinburgh, Edinburgh, UK;(3) Center for Theoretical Neuroscience, Columbia University, New York, NY, USA |
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Abstract: | We recently introduced likelihood-based methods for fitting stochastic integrate-and-fire models to spike train data. The
key component of this method involves the likelihood that the model will emit a spike at a given time t. Computing this likelihood is equivalent to computing a Markov first passage time density (the probability that the model
voltage crosses threshold for the first time at time t). Here we detail an improved method for computing this likelihood, based on solving a certain integral equation. This integral
equation method has several advantages over the techniques discussed in our previous work: in particular, the new method has
fewer free parameters and is easily differentiable (for gradient computations). The new method is also easily adaptable for
the case in which the model conductance, not just the input current, is time-varying. Finally, we describe how to incorporate
large deviations approximations to very small likelihoods.
Action Editor: Barry J. Richmond |
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Keywords: | Volterra integral equation Markov process Large deviations approximation |
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