System identification (2nd ed.): theory for the user
System identification (2nd ed.): theory for the user
Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems
Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems
Generating spike trains with specified correlation coefficients
Neural Computation
Adaptive contrast gain control and information maximization
Neurocomputing
Multivariate autoregressive modeling and granger causality analysis of multiple spike trains
Computational Intelligence and Neuroscience - Special issue on signal processing for neural spike trains
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Linear-Nonlinear-Poisson (LNP) models are a popular and powerful tool for describing encoding (stimulus-response) transformations by single sensory as well as motor neurons. Recently, there has been rising interest in the second- and higher-order correlation structure of neural spike trains, and how it may be related to specific encoding relationships. The distortion of signal correlations as they are transformed through particular LNP models is predictable and in some cases analytically tractable and invertible. Here, we propose that LNP encoding models can potentially be identified strictly from the correlation transformations they induce, and develop a computational method for identifying minimum-phase single-neuron temporal kernels under white and colored random Gaussian excitation. Unlike reverse-correlation or maximum-likelihood, correlation-distortion based identification does not require the simultaneous observation of stimulus-response pairs--only their respective second order statistics. Although in principle filter kernels are not necessarily minimum-phase, and only their spectral amplitude can be uniquely determined from output correlations, we show that in practice this method provides excellent estimates of kernels from a range of parametric models of neural systems. We conclude by discussing how this approach could potentially enable neural models to be estimated from a much wider variety of experimental conditions and systems, and its limitations.