## Sequential optimal design of neurophysiology
experiments

Neural Computation 21: 619-687.

Adaptively optimizing experiments has the potential to significantly
reduce the number of trials needed to build parametric statistical
models of neural systems. However, application of adaptive methods to
neurophysiology has been limited by severe computational
challenges. Since most neurons are high dimensional systems,
optimizing neurophysiology experiments requires computing
high-dimensional integrations and optimizations in real time. Here we
present a fast algorithm for choosing the most informative stimulus by
maximizing the mutual information between the data and the unknown
parameters of a generalized linear model (GLM) which we want to fit to
the neuron's activity. We rely on important log-concavity and
asymptotic normality properties of the posterior to facilitate the
required computations. Our algorithm requires only low-rank matrix
manipulations and a 2-dimensional search to choose the optimal
stimulus. The average running time of these operations scales
quadratically with the dimensionality of the GLM, making real-time
adaptive experimental design feasible even for high-dimensional
stimulus and parameter spaces. For example, we require roughly 10
milliseconds on a desktop computer to optimize a 100-dimensional
stimulus. Despite using some approximations to make the algorithm
efficient, our algorithm asymptotically decreases the uncertainty
about the model parameters at a rate equal to the maximum rate
predicted by an asymptotic analysis. Simulation results show that
picking stimuli by maximizing the mutual information can speed up
convergence to the optimal values of the parameters by an order of
magnitude compared to using random (nonadaptive) stimuli. Finally,
applying our design procedure to real neurophysiology experiments
requires addressing the nonstationarities that we would expect to see
in neural responses; our algorithm can efficiently handle both fast
adaptation due to spike-history effects and slow, non-systematic
drifts in a neuron's activity.

Reprint | Related work
on active learning | Liam Paninski's research page