Journal of Computational Neuroscience

, Volume 29, Issue 1, pp 89-105

First online:

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

  • Shinsuke KoyamaAffiliated withDepartment of Statistics and Center for the Neural Basis of Cognition, Carnegie Mellon University Email author 
  • , Liam PaninskiAffiliated withDepartment of Statistics and Center for Theoretical Neuroscience, Columbia University

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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.


Tridiagonal Newton–Raphson method Laplace approximation State-space models Point processes