High-dimensional neural spike train analysis with generalized count linear dynamical systems
Latent factor models have been widely used to analyze simultaneous recordings of spike trains from large, heterogeneous neural populations. These models assume the signal of interest in the population is a low-dimensional latent intensity that evolves over time, which is observed in high dimension via noisy point-process observations. These techniques have been well used to capture neural correlations across a population and to provide a smooth, denoised, and concise representation of high-dimensional spiking data. One limitation of many current models is that the observation model is assumed to be Poisson, which lacks the flexibility to capture under-and over-dispersion that is common in recorded neural data, thereby introducing bias into estimates of covariance. Here we develop the generalized count linear dynamical system, which relaxes the Poisson assumption by using a more general exponential family for count data. In addition to containing Poisson, Bernoulli, negative binomial, and other common count distributions as special cases, we show that this model can be tractably learned by extending recent advances in variational inference techniques. We apply our model to data from primate motor cortex and demonstrate performance improvements over state-of-the-art methods, both in capturing the variance structure of the data and in held-out prediction.
High-dimensional neural spike train analysis with generalized count linear dynamical systemsThis paper describes a general exponential-family model (called the "generalized count" (GC) distribution) for multi-neuron spike count data. The model accounts for both under-dispersed and over-dispersed spike count data, and has Poisson, Negative Binomial, Bernoulli, and several other classic models as special cases.The authors give a clear account of the relationship to other models, and demonstrate the need for a model to capture under-dispersed counts in primate motor cortex.They then describe an efficient method for maximum-likelihood fitting (and demonstrate concavity of the log-likelihood).It briefly discusses GC regression before turning to latent variable modeling of population data using a latent Gaussian linear dynamical system and GC observations.They derive an efficient variational Bayesian inference method and apply the model to data from primate motor cortex, showing that it accounts more accurately for variance and cross-covariance of spike count data, compared to a model with Poisson observations.The paper is clearly written, original, interesting, and thorough, and likely to have a major impact on the field of neural coding and latent variable modeling of neural data. While the quantitative improvement over existing models is somewhat modest, the model has very nice theoretical properties and is attractive for its ability to account for under- and over-dispersion within a single framework. An outstanding paper -- I expect it to attract considerable interest and attention.If I have one general criticism it's that it would be nicer to have a clearer idea for how to model single-neuron data, since the "full" model assigns zero probability to all unobserved counts (sending test log-likelihood negative infinity if the test data ever contains a count not observed in training), and the "simple" model requires a full population.The authors mention this shortcoming briefly in the discussion, but it might be nice to have a simple recommendation for how to handle this (e.g., add a small pseudocount for some reasonable set of possible spike counts). Technical comments:106: "this choice has been previously considered and found suboptimal [8]".No no no, that is not correct! I'm sorry, the Macke et al 2011 paper did NOT examine a fine timescale GLM at all, much less whether it could account for underdispersion (or cross-correlations) in population data. The smallest bin size used was 10ms (which is obviously too big to be effective for modeling short time-scale refractory effects).So please stop repeating this misleading claim from that earlier paper.Besides, there's no need for this attack here: this paper addresses an interesting and important problem its own right, whether or not there's some other approach for capturing underdispersion that might also suffice.(Someone should make a sincere attempt, but it's a topic for another paper.)Table 1:If you have space, it might be nice to include the mapping to \theta in the "GCGLM Parametrization", just to make it easier for people to mentally connect the GC model to the classic models.(e.g., \theta = \log \lambda for Poisson model). Not strictly necessary though if it takes too much space.eq 6: I found this a little puzzling when I first read it -- might be helpful to spell out what g_i is.294: "does not significantly overfit"?This is for how much data -- the same amount as the recording data?(Presumably there should be substantial overfitting for a small dataset.)Fig 2: is this all from training data (i.e., just confirming that the model is capable of exhibiting the desired mean-variance relationship), or is there some prediction on test data underlying this figure?