Title: Fast neural encoding model estimation via expected log-likelihoods
Receptive fields are traditionally measured using the spike-triggered average (STA). Recent work has shown that the STA is a special case of a family of estimators derived from the “expected log-likelihood” of a Poisson model. We generalize these results to the broad class of neuronal response models known as generalized linear models (GLM). We show that expected log-likelihoods can speed up by orders of magnitude computations involving the GLM log-likelihood, e.g parameter estimation, marginal likelihood calculations, etc., under some simple conditions on the priors and likelihoods involved. Second, we perform a risk analysis, using both analytic and numerical methods, and show that the “expected log- likelihood” estimators come with a small cost in accuracy compared to standard MAP estimates. When MAP accuracy is desired, we show that running a few pre-conditioned conjugate gradient iterations on the GLM log-likelihood initialized at the "expected log-likelihood" can lead to an estimator that is as accurate as the MAP. We use multi-unit, primate retinal responses to stimuli with naturalistic correlation to validate our findings.
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