  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.
