Efficient, adaptive estimation of two-dimensional firing rate
surfaces via Gaussian process methods
In press, Network
Estimating two-dimensional firing rate maps is a common problem,
arising in a number of contexts: the estimation of place fields in
hippocampus, the analysis of temporally nonstationary tuning curves in
sensory and motor areas, the estimation of firing rates following
spike-triggered covariance analyses, etc. Here we introduce methods
based on Gaussian process nonparametric Bayesian techniques for
estimating these two-dimensional rate maps. These techniques offer a
number of advantages: the estimates may be computed efficiently, come
equipped with natural errorbars, adapt their smoothness automatically
to the local density and informativeness of the observed data, and
permit direct fitting of the model hyperparameters (e.g., the prior
smoothness of the rate map) via maximum marginal likelihood. We
illustrate the flexibility and performance of the new techniques on a
variety of simulated and real data.
Preprint (pdf, 700K) | Liam Paninski's home