Maximum Likelihood Estimation of a Stochastic Integrate-and-Fire Neural Encoding Model

• Published in: Neural computation Vol. 16; no. 12; pp. 2533 - 2561
• Main Authors: Paninski, Liam, Pillow, Jonathan W., Simoncelli, Eero P.
• Format: Journal Article
• Language: English
• Published: One Rogers Street, Cambridge, MA 02142-1209, USA MIT Press 01.12.2004; MIT Press Journals, The
• Subjects: Algorithms; Applied sciences; Artificial intelligence; Biological and medical sciences; Biophysical Phenomena; Biophysics; Computer science; control theory; systems; Electrophysiology; Estimates; Exact sciences and technology; Fundamental and applied biological sciences. Psychology; General aspects; Inference from stochastic processes; time series analysis; Learning and adaptive systems; Likelihood Functions; Mathematics; Mathematics in biology. Statistical analysis. Models. Metrology. Data processing in biology (general aspects); Maximum likelihood method; Membrane Potentials; Models, Neurological; Models, Statistical; Neurons; Neurons - physiology; Nonlinear Dynamics; Poisson Distribution; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications); Statistics; Stochastic models; Density estimation; Stochastic model; Neural computation; Neuronal discharge; Cascade encoding; Log likelihood; Linear filtering; Numerical simulation; Maximum likelihood; Neural network; Computing; Likelihood function
• ISSN: 0899-7667; 1530-888X
• DOI: 10.1162/0899766042321797

We examine a cascade encoding model for neural response in which a linear filtering stage is followed by a noisy, leaky, integrate-and-fire spike generation mechanism. This model provides a biophysically more realistic alternative to models based on Poisson (memoryless) spike generation, and can effectively reproduce a variety of spiking behaviors seen in vivo. We describe the maximum likelihood estimator for the model parameters, given only extracellular spike train responses (not intracellular voltage data). Specifically, we prove that the log-likelihood function is concave and thus has an essentially unique global maximum that can be found using gradient ascent techniques. We develop an efficient algorithm for computing the maximum likelihood solution, demonstrate the effectiveness of the resulting estimator with numerical simulations, and discuss a method of testing the model's validity using time-rescaling and density evolution techniques.