Efficient computation of the maximum a posteriori path and parameter estimation in integrate-and-fire and more general state-space models.
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.
Koyama
Shinsuke
S
Department of Statistics and Center for the Neural Basis of Cognition, Carnegie Mellon University, Pittsburgh, PA, USA. koyama@stat.cmu.edu.
Paninski
Liam
L
Department of Statistics and Center for Theoretical Neuroscience, Columbia University, New York, NY, USA.
D000200:Action Potentials / Q000502:physiology; D000465:Algorithms; D000818:Animals; D003198:Computer Simulation; D008959:Models, Neurological; D015233:Models, Statistical; D009474:Neurons / Q000502:physiology*