Identification of interacting neural populations: methods and statistical considerations.

As improved recording technologies have created new opportunities for neurophysiological investigation, emphasis has shifted from individual neurons to multiple populations that form circuits, and it has become important to provide evidence of cross-population coordinated activity. We review various methods for doing so, placing them in six major categories while avoiding technical descriptions and instead focusing on high-level motivations and concerns. Our aim is to indicate what the methods can achieve and the circumstances under which they are likely to succeed. Toward this end, we include a discussion of four cross-cutting issues: the definition of neural populations, trial-to-trial variability and Poisson-like noise, time-varying dynamics, and causality.

Oscillating neural circuits: Phase, amplitude, and the complex normal distribution.

Multiple oscillating time series are typically analyzed in the frequency domain, where coherence is usually said to represent the magnitude of the correlation between two signals at a particular frequency. The correlation being referenced is complex-valued and is similar to the real-valued Pearson correlation in some ways but not others. We discuss the dependence among oscillating series in the context of the multivariate complex normal distribution, which plays a role for vectors of complex random variables analogous to the usual multivariate normal distribution for vectors of real-valued random variables. We emphasize special cases that are valuable for the neural data we are interested in and provide new variations on existing results. We then introduce a complex latent variable model for narrowly band-pass-filtered signals at some frequency, and show that the resulting maximum likelihood estimate produces a latent coherence that is equivalent to the magnitude of the complex canonical correlation at the given frequency. We also derive an equivalence between partial coherence and the magnitude of complex partial correlation, at a given frequency. Our theoretical framework leads to interpretable results for an interesting multivariate dataset from the Allen Institute for Brain Science.

Les séries temporelles à oscillations multiples sont généralement étudiées dans le domaine fréquentiel, où la cohérence est souvent considérée comme l'amplitude de la corrélation entre deux signaux à une fréquence spécifique. Cette corrélation est à valeurs complexes et présente des similitudes avec la corrélation de Pearson pour les valeurs réelles, tout en présentant des différences distinctes. Dans cette étude, les auteurs explorent la dépendance entre les séries oscillantes en utilisant la distribution normale complexe multivariée. Cette distribution est l'équivalent de la distribution normale multivariée classique, mais adaptée aux vecteurs de variables aléatoires complexes plutôt qu'aux vecteurs de variables aléatoires réelles. Les auteurs mettent l'accent sur des cas spécifiques qui revêtent une importance particulière pour les données neuronales qui les intéressent, tout en proposant de nouvelles approches et des variations des résultats existants. Ils introduisent un modèle de variables latentes complexes pour les signaux filtrés en bande passante étroite à une fréquence donnée. Ils démontrent ensuite que l'estimation du maximum de vraisemblance dans ce modèle produit une cohérence latente équivalente à l'amplitude de la corrélation canonique complexe à la fréquence spécifiée. Ils établissent également une équivalence entre la cohérence partielle et l'amplitude de la corrélation partielle complexe, toujours à une fréquence donnée. Leur approche théorique conduit à des résultats interprétables pour un ensemble de données multivariées intéressant provenant de l'Allen Institute for Brain Science.

Latent Dynamic Factor Analysis of High-Dimensional Neural Recordings.

High-dimensional neural recordings across multiple brain regions can be used to establish functional connectivity with good spatial and temporal resolution. We designed and implemented a novel method, Latent Dynamic Factor Analysis of High-dimensional time series (LDFA-H), which combines (a) a new approach to estimating the covariance structure among high-dimensional time series (for the observed variables) and (b) a new extension of probabilistic CCA to dynamic time series (for the latent variables). Our interest is in the cross-correlations among the latent variables which, in neural recordings, may capture the flow of information from one brain region to another. Simulations show that LDFA-H outperforms existing methods in the sense that it captures target factors even when within-region correlation due to noise dominates cross-region correlation. We applied our method to local field potential (LFP) recordings from 192 electrodes in Prefrontal Cortex (PFC) and visual area V4 during a memory-guided saccade task. The results capture time-varying lead-lag dependencies between PFC and V4, and display the associated spatial distribution of the signals.