Efficient computation of the
maximum a posteriori path and parameter estimation in
integrate-and-fire and more general state-space models
In press, Journal of Computational Neuroscience, special issue on
statistical analysis of neural data
A number of important data analysis problems in neuroscience can be
solved using state-space models. In this article, we describe fast
methods for computing the exact maximum a posteriori (MAP) path of the
hidden state variable in these models, given spike train observations.
If the state transition density is log-concave and the observation
model satisfies certain standard assumptions, then the optimization
problem is strictly concave and can be solved rapidly with
Newton-Raphson methods, because the Hessian of the loglikelihood is
block tridiagonal. We can further exploit this block-tridiagonal
structure to develop efficient parameter estimation methods for these
models. We describe applications of this approach to neural decoding
problems, with a focus on the classic integrate-and-fire model as a
key example.
Preprint (600K,
pdf) | Related work on
integrate-and-fire models | Liam Paninski's home