Paper:
Real-Time Inference for a Gamma Process Model of Neural Spiking 1
With simultaneous measurements from ever increasing populations of neurons, there is a growing need for sophisticated tools to recover signals from individual neurons. In electrophysiology experiments, this classically proceeds in a two-step process: (i) threshold the waveforms to detect putative spikes and (ii) cluster the waveforms into single units (neurons). We extend previous Bayesian nonparametric models of neural spiking to jointly detect and cluster neurons using a Gamma process model. Importantly, we develop an online approximate inference scheme enabling real-time analysis, with performance exceeding the previous state-of-theart. Via exploratory data analysis-using data with partial ground truth as well as two novel data sets-we find several features of our model collectively contribute to our improved performance including: (i) accounting for colored noise, (ii) detecting overlapping spikes, (iii) tracking waveform dynamics, and (iv) using multiple channels. We hope to enable novel experiments simultaneously measuring many thousands of neurons and possibly adapting stimuli dynamically to probe ever deeper into the mysteries of the brain.

Review:
This paper introduces a Bayesian nonparametric method 
      to address the problem of spike detection and sorting (i.e. for jointly 
      detecting neural spikes and assigning them to neurons). These steps are 
      naturally of critical importance to many computational models of neural 
      spiking data as they essentially create the 'ground truth' data on which 
      many models operate. Improving these methods thus is of great interest to 
      the wider computational neuroscience community. The authors develop an 
      efficient online method based on the gamma process that models both the 
      waveforms of spikes for each neuron and the assignment of spikes to 
      neurons. The use of a Chinese restaurant process elegantly allows the 
      model to add new neurons (i.e. the number of neurons from which spikes are 
      detected does not need to be specified a priori). There are some neat 
      features to the model, such as the ability to model non-stationary 
      waveforms (i.e. varying over time). The authors perform an empirical 
      comparison to previous state of the art approaches that provides a 
      compelling case for their method and provide an interesting discussion. 
      Quality: The authors derive a model that is conceptually quite 
      complex although neat and appears correct. The novel concepts, methods and 
      empirical analysis are of high quality. The writing should be improved on 
      (this perhaps falls under the clarity category) particularly to clarify 
      the model, although this can be done for a camera ready. Clarity: 
      As stated above, the model is rather complex. The authors try to 
      explain the model by starting with simpler models (i.e. a homogenous 
      Poisson process) and then in a step by step fashion add complexity and 
      draw connections to various distributions until they arrive to what their 
      model actually is. I believe this is an attempt to explain their approach 
      to the reader in an accessible way, but I feel it is somewhat confusing. 
      Rather than draw parallels to the entire Bayesian nonparametrics toolbox, 
      it would be better in my opinion to state what the actual model is and 
      then explain the assumptions taken to arrive at this model. I think this 
      is also an opportunity to reclaim a significant amount of space (which is 
      clearly scarce here) which can be used to put in a diagram (graphical 
      model) of the model(s) introduced in this paper. Originality: 
      This appears to be original work and addresses some shortcomings of 
      previous approaches. There are similar approaches to spike sorting (e.g. 
      the Dirichlet process mixture models for spike sorting of Gasthaus et 
      al.). However, this paper makes significantly more than delta changes to 
      those works in the model, in how it adapts the waveforms and performs real 
      time spike sorting using variational Bayesian methods. 
      Significance: As stated above, spike sorting and detecting are 
      two critical early steps in the computational neuroscience modeling 
      pipeline. Thus improving accuracy would be very useful to many 
      computational models which analyse the data resulting from these steps and 
      improving speed can significantly help achieve real time decoding and move 
      towards larger populations of neurons. Detailed comments: 48: 
      inference -> infer 52: develop -> developing 58: that that 
      77: It sounds a bit strange to say that you 'relax' simplifying 
      assumptions - i.e. sounds like you make them simpler 79: as -> are 
      90: Rather that -> Rather than 163: The mean and covariance are 
      drawn from a Wishart distribution, of which the parameters are drawn from 
      the CRP correct? Perhaps you should add another line in the equation array 
      to make this clear. 183: Twiddles is not a word I am familiar with. 
      Tildes? 184: Associate -> Associated 185: in -> is 197: 
      the subvector 209: I really appreciate Algorithm 1 - I think this 
      should be in the main text if you can find space 224: case a -> 
      case of a 424: being estimates? 428: "embarassingly" parallel 
      sounds rather colloquial and sarcastic The paper states that code 
      is provided in the supplementary materials to run the models introduced in 
      the paper. I would like to run this code to verify but I can't find it in 
      the supplementaries. A reference that motivates the importance of 
      waveform non-stationarity. G. Santhanam, M. D. Linderman, V. Gilja, A. 
      Afshar, S. I. Ryu, T. H. Meng, and K. V. Shenoy. HermesB: A continuous 
      neural recording system for freely behaving primates. IEEE Transactions on 
      Biomedical Engineering, 54(11):2037–2050, 2007. One concern of 
      this reviewer in the nature of the empirical evaluation is that the ground 
      truth is from only on a single neuron from a single data set. Naturally, I 
      sympathize that obtaining such data is rather difficult and we are lucky 
      that even this ground truth data exists and is provided online. However, 
      it does raise a number of concerns - is it possible that we can overfit as 
      a community if we all attempt to achieve state of the art on this single 
      neuron. Furthermore, what is the guarantee that the assumptions made in 
      this work hold for this particular neuron (or a particular class) but 
      don't for others (e.g. we know different classes of neuron exhibit very 
      different patterns of behavior). It may be useful to state that 
      [23] compares empirically to a number of models that your method doesn't 
      directly compare to such as [27]. So although not comparing directly to 
      that work you are more or less comparing by 
      proxy.