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

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. Keywords Tridiagonal Newton-Raphson method

• Type: Journal
• Year: 2010
• Where: JCNS
• Authors: Shinsuke Koyama, Liam Paninski
• Keywords: Certain Standard Assumptions, Data Analysis Problems, JCNS 2010, Parameter Estimation Methods