MODELING NEURAL SPIKING WITH POINT PROCESSES
NONPARAMETRICALLY: A CONVEX OPTIMIZATION APPROACH
Todd P Coleman, UIUC
Sridevi Sarma, MIT
www.csl.uiuc.edu
colemant@uiuc.edu
sree@mit.edu
Characterizing neural spiking activity as a function of environmental stimuli, and intrinsic effects such as a neuron's own spiking history and
concurrent ensemble activity is important in neuroscience. Such a characterization is complex and there is increasing need for a broad class of
models to capture such details. Point process models have been shown to be very useful in characterizing neural spiking activity [Brown et al 03].
How do we select the best Lipschitz constant K?
Memory Data
To date, most models are parametric and thus rely on many assumptions. Nonparametric methods are attractive due to fewer assumptions, but very few
efficient methods for these scenarios are known. We propose a computationally efficient maximum-likelihood estimation methodology under mild
smoothness assumptions. It relies on convex optimization and admits complexity reduction through Lagrangian duality. We use the Time-Rescaling
Theorem for goodness-of-fit analysis and model selection.
Closed-form Dual Optimization Problem
Equivalent Computationally Efficient Closed-Form Dual Problem
Can be efficiently solved using a
nondifferentiable convex optimization
approach involving subgradient
projections
Calculation of each subgradient only
involves executing a network flow
problem to return a dual optimal solution
References
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Neuroscience: A Comprehensive Approach. London: CRC, 2003; Chapter 9, pp 253-286.
•D. Daley and D. Vere-Jones. An Introduction to the theory of point processes. Springer-Verlag, NewYork, 2003.
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