Correlation-distortion based identification of Linear-Nonlinear-Poisson models

TL;DR

This paper introduces a novel correlation-distortion based method for identifying Linear-Nonlinear-Poisson (LNP) neural models using only second-order statistics, enabling model estimation without stimulus-response pairs.

Contribution

It develops a new computational approach for LNP model identification based on correlation transformations, applicable under various excitation conditions and not requiring stimulus-response data.

Findings

Accurately estimates neural kernels from simulated data.

Works with both white and colored Gaussian stimuli.

Provides a practical alternative to existing methods.

Abstract

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.