Extracting Latent Structure From Multiple Interacting Neural Populations
Developments in neural recording technology are rapidly enabling the recording of populations of neurons in multiple brain areas simultaneously, as well as the identification of the types of neurons being recorded (e.g., excitatory vs. inhibitory). There is a growing need for statistical methods to study the interaction among multiple, labeled populations of neurons. Rather than attempting to identify direct interactions between neurons (where the number of interactions grows with the number of neurons squared), we propose to extract a smaller number of latent variables from each population and study how these latent variables interact. Specifically, we propose extensions to probabilistic canonical correlation analysis (pCCA) to capture the temporal structure of the latent variables, as well as to distinguish within-population dynamics from across-population interactions (termed Group Latent Auto-Regressive Analysis, gLARA). We then applied these methods to populations of neurons recorded simultaneously in visual areas V1 and V2, and found that gLARA provides a better description of the recordings than pCCA. This work provides a foundation for studying how multiple populations of neurons interact and how this interaction supports brain function.
It is becoming feasible to obtain cellular recordings with large numbers of cells simultaneously. In particular, this submission focuses on analysis when multiple populations of cells are recorded simultaneously (population being perhaps multiple brain areas, or cell types). In particular, they build latent variable models to describe the interactions between two, simultaneously recorded, neuronal populations.The baseline method for modelling interactions between populations with latent variables is pCCA. However, CCA only captures instantaneous interactions, and does not capture any temporal structure.The submission introduces AR-CCA, which defines a autoregressive linear-Guassian model on the latent state. In addition, they introduce gLARA which constrains the covariance structure by removing shared latent variables. They describe an expectation-maximization approach to fitting the model.The authors then examine the efficacy of the models for describing a neuronal recording of V1 and V2 (actually the residuals after subtracting the PSTH). First, they demonstrated that pCCA, which distinguishes between within-population and between-population covariances is able to capture the data with many fewer latent variables than factor analysis (which does not distinguish).Using cross-validation, they demonstrate that (unsurprisingly) AR-pCCA and gLARA, which contain dynamics are better able to model the data. gLARA is slightly better, which would indicate that the additional constraints in the model are helping to prevent overfitting. Finally, they examine the temporal structure of interactions between V1 and V2.QualityThe claims made are well-supported by the evidence. The choice of pCCA is a reasonable baseline for comparison.ClarityThe submission is well-written. In particular, the motivations behinds models and relationships between them is explained well which is very helpful for comprehension.OriginalityThe manuscript introduces a new model AR-CCA which combines CCA with dynamics to allow capture relationships in sequential data. This is original, and the authors demonstrate its efficacy (along with the more constrained gLARA) in capturing neuronal interactions.SignificanceThe submission is of primary interest to a specialised audience. While it is true that high-dimensional neuronal recordings are becoming increasingly common, the models presented are only relevant when multiple populations (known to the experimenter) are recorded simultaneously. Additionally, while the authors showed their models capture neuronal statistics (i.e. did well in cross-validation) it wasn’t clear what biological insights such models conveyed (for example, what does figure 5 help us understand about V1/V2 function). It would be helpful to at least speculate on this topic.