Paper:
Bayesian latent structure discovery from multi-neuron recordings
Neural circuits contain heterogeneous groups of neurons that differ in type, location, connectivity, and basic response properties. However, traditional methods for dimensionality reduction and clustering are ill-suited to recovering the structure underlying the organization of neural circuits. In particular, they do not take advantage of the rich temporal dependencies in multi-neuron recordings and fail to account for the noise in neural spike trains. Here we describe new tools for inferring latent structure from simultaneously recorded spike train data using a hierarchical extension of a multi-neuron point process model commonly known as the generalized linear model (GLM). Our approach combines the GLM with flexible graph-theoretic priors governing the relationship between latent features and neural connectivity patterns. Fully Bayesian inference via Pólya-gamma augmentation of the resulting model allows us to classify neurons and infer latent dimensions of circuit organization from correlated spike trains. We demonstrate the effectiveness of our method with applications to synthetic data and multi-neuron recordings in primate retina, revealing latent patterns of neural types and locations from spike trains alone.

Review:
The authors describe a statistical model of neural data that combines random network models (distributions over the connections and weights between neurons) with a standard point process spiking model, a generalized linear model (GLM). By restricting the spiking process to logistic spike count models, the authors apply the Polya-gamma augmentation trick to perform efficient inference through Gibbs sampling. The authors apply their technique to simulated data (recovering latent network structure in the simulated network) and to spiking activity of retinal ganglion cells (RGCs). This technique lets the authors quantitatively reason over network connectivity, providing a way to reason about hypotheses regarding how network structure relates to recorded neural activity.
In general, the motivation, model, and experiments are clearly described and well presented.  The usefulness of the application to retinal data is overstated. In the second paragraph, the authors mention that there are a "plethora of RGC types" that have been identified and then go on to discuss that their method will "automatically discover this structure from correlated patterns of neural activity". This is incorrect for two reasons: First, the authors demonstrate that their method only discovers two RGC types (the standard ON vs OFF classification) and their results do not recover the "plethora of RGC types" mentioned in the introduction. Secondly, at least in the retina, the network activity is directly tied to the stimulus--and the experimental choice of stimulus--and therefore their method is, implicitly, tied to the choice of stimulus. For example, consider if the experiment had used a full field stimulus or only concentrated the stimulus on a small part of the visual field. Then, the network activity (and resulting conclusions of the modeling effort) would be markedly different. I am just pointing out that when analyzing responses of sensory areas the analysis is not independent of the stimulus, and the authors should discuss and highlight the implications of the experimental stimulus.  Another point about the application to retinal data--the authors make a point of highlighting that their methods discover ON and OFF cell types in the data without knowledge of the stimulus using a minute of data (first paragraph of section 5). However, experimentally, we *do* have access to the stimulus (in fact, we choose it) and it does not make sense to perform stimulus independent analysis (especially for something like the discovery of OFF or ON cell types, which can be done in seconds using a light and dark flash stimulus).  However, I do recognize that the stimulus independent analysis is very useful in two very important contexts: (1) deeper in the brain, where the relevant stimulus may be unknown or hard to control, and (2) in sensory recordings in response to uncontrolled stimuli, such as natural stimuli. These are both scenarios where the techniques put forth in this paper could prove to be powerful ways of identifying latent structure that has been difficult to crack using more conventional stimulus-response modeling approaches. I think making this point explicit in the introduction or conclusion would further strengthen the motivations of the paper.  As a final point on the comparison to retinal data, I would appreciate if the authors compared their technique to some naive baselines. For example, the correlation between the spike trains of two cells drops off with distance in the retina. If one simply used the spike train correlation as an estimate of distance, how would that compare to the NGLM approach in Figure 4b? In addition, how does the network structure compare to a simpler approach of the MAP estimate of a GLM with l1 or l2 priors on the coupling terms? The authors mention this simple model at the end of section 2.2, it would be nice to know how inferred network structure from a regularized GLM compares to their NGLM technique.  I would have appreciated more discussion surrounding the types of network models used (e.g. the stochastic block model and latent distance model). These were introduced very briefly in section 2.3, and I would have appreciated more explanation of what kinds of latent structure these descriptions could capture and how they relate to existing hypotheses of connectivity in neural systems.  In general, the paper is well written, I enjoyed reading it, and it raises interesting questions about how to model network structure given recorded spiking activity. To really demonstrate the advantages of their approach, more comparisons to simpler and existing approaches are needed. More discussion about how their methods will be relevant for other neural systems besides the retina is also welcome.