Maximum likelihood estimation of a stochastic
integrate-and-fire neural model
Presented (as a talk) at:
Neural Information Processing Systems (NIPS*03), Vancouver BC, Dec 2003.
Published in:
Advances in Neural Information Processing Systems 16
eds. S. Thrun, L. Saul, and B. Schölkopf, May 2004.
doi: 10.1162/0899766042321797
© MIT Press, Cambridge, MA.
Recent work has examined the estimation of models of stimulus-driven
neural activity in which some linear filtering process is followed by a
nonlinear, probabilistic spiking stage. We analyze the estimation of one
such model for which this nonlinear step is implemented by a noisy,
leaky, integrate-and-fire mechanism with a spike-dependent after-current.
This model is a biophysically plausible alternative to models with
Poisson (memory-less) spiking, and has been shown to effectively
reproduce various spiking statistics of neurons in vivo. However, the
problem of estimating the model from extracellular spike train data has
not been examined in depth. We formulate the problem in terms of maximum
likelihood estimation, and show that the computational problem of
maximizing the likelihood is tractable. Our main contribution is
an algorithm and a proof that this algorithm is guaranteed to find the
global optimum with reasonable speed. We demonstrate the effectiveness
of our estimator with numerical simulations.
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