Review for NeurIPS paper: Online Neural Connectivity Estimation with Noisy Group Testing

Summary and Contributions: This paper presents an approach to the problem of inferring a functional network across many neurons using noisy group testing. The authors formulate the connections across a population of neurons as a binary network that encodes the presence or absence of functional (not necessarily synaptic) connections between pairs of neurons, with a noisy Bernoulli observation model to capture neurons occasionally not being activated even when neurons they are functionally connected to are stimulated. Inference over the connections is initially formulated as a maximum likelihood problem, which can be rewritten as an integer optimization problem. The authors further extend this formulation by relaxing the variables to restricted continuous values and reformulating the problem as approximate Bayesian inference to infer the posterior probability of each connection. A dual decomposition algorithm is presented for solving the problem, which can be adapted to perform online inference in the setting where an experimenter might want to update the posterior probabilities as new tests are performed or adaptively select tests based on the current network estimate.