Efficient computation of the maximum a posteriori path and parameter estimation in integrate-and-fire and more general state-space models

Authors:
Shinsuke Koyama;Liam Paninski
Affiliations:
Department of Statistics and Center for the Neural Basis of Cognition, Carnegie Mellon University, Pittsburgh, USA;Department of Statistics and Center for Theoretical Neuroscience, Columbia University, New York, USA
Venue:
Journal of Computational Neuroscience
Year:
2010

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Abstract

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.