  Inferring connectivity in neuronal networks remains a key challenge in
statistical neuroscience. The `common input' problem presents the major
roadblock: it is difficult to reliably distinguish causal connections between
pairs of observed neurons from correlations induced by common input from
unobserved neurons. Since available recording techniques allow us to sample
from only a small fraction of large networks simultaneously with sufficient
temporal resolution, naive connectivity estimators that neglect these common
input effects are highly biased. This work proposes a `shotgun' experimental
design, in which we observe multiple sub-networks briefly, in a serial manner.
Thus, while the full network cannot be observed simultaneously at any given
time, we may be able to observe most of it during the entire experiment. Using
a generalized linear model for a spiking recurrent neural network, we develop
scalable approximate Bayesian methods to perform network inference given this
type of data, in which only a small fraction of the network is observed in each
time bin. We demonstrate in simulation that, using this method: (1) The shotgun
experimental design can eliminate the biases induced by common input effects.
(2) Networks with thousands of neurons, in which only a small fraction of the
neurons is observed in each time bin, could be quickly and accurately
estimated. (3) Performance can be improved if we exploit prior information
about the probability of having a connection between two neurons, its
dependence on neuronal cell types (e.g., Dale's law), or its dependence on the
distance between neurons.
