Paper:
Clustered factor analysis of multineuronal spike data
High-dimensional, simultaneous recordings of neural spiking activity are often explored, analyzed and visualized with the help of latent variable or factor models. Such models are however ill-equipped to extract structure beyond shared, distributed aspects of firing activity across multiple cells. Here, we extend unstructured factor models by proposing a model that discovers subpopulations or groups of cells from the pool of recorded neurons. The model combines aspects of mixture of factor analyzer models for capturing clustering structure, and aspects of latent dynamical system models for capturing temporal dependencies. In the resulting model, we infer the subpopulations and the latent factors from data using variational inference and model parameters are estimated by Expectation Maximization (EM). We also address the crucial problem of initializing parameters for EM by extending a sparse subspace clustering algorithm to integer-valued spike count observations. We illustrate the merits of the proposed model by applying it to calcium-imaging data from spinal cord neurons, and we show that it uncovers meaningful clustering structure in the data.

Review:
The paper proposes a method for clustering multi-neuronal data based on a parametric latent variable model. The main contribution of the approach presented is the extension of previous mixture of factor analyzers models to a dynamic setup where a hidden latent model captures the temporal structure of the model. Latent variable models have proven very successful in recent years, and offer great flexibility and lead to efficient (usually approximate) estimation algorithms.  The basic building block of the model is a multinomial population model allowing each neuron to belong to one of M classes, where each latent variable is modeled using a linear dynamical system, and the observation model is based on a Poisson firing model. The main distinction compared to previous work is the incorporation of temporal dependencies in the latent variables. The general inference and parameter estimation is intractable within the present setting, leading to the introduction of a factorization assumption for the posterior distribution, and to a variational lower bound. This lower bound is optimized based on coordinate ascent, which is facilitated by using the dual formulation. The parameter update is interleaved with the update of the variational bound variables, leading to a variational EM type algorithm. In order to improve performance, an initialization scheme is proposed based on Poisson subspace sampling.  Additionally, in order to prevent certain undesirable properties of the solution (like assigning all neurons to a single cluster), a non-negativity constraint is introduced into the neuronal activity model. The authors conclude their paper by presenting experiments with both artificial and natural data, taken from calcium imaging of motor neurons activities. The analysis of the empirical data led to some interesting conclusions about the firing phase of neurons. Interestingly, validation using electro-physiological measurements was suggested, opening an interesting route for model validation. Overall this is a solid paper, extending earlier work in several promising directions and demonstrating good empirical results. However, as far as NIPS paper go, the contribution beyond previous work seems rather incremental.A question that should be addressed:The model described in eqs. (3-5) is linear and assumed a specific noise model. What are the implications of these assumptions? How robust is the model to misspecification? Following the authors' response I have re-evaluated the contribution of the paper and raised my original score.