Abstract
Advances in multi-unit recordings pave the way for statistical modeling of activity patterns in large neural populations. Recent studies have shown that the summed activity of all neurons strongly shapes the population response. A separate recent finding has been that neural populations also exhibit criticality, an anomalously large dynamic range for the probabilities of different population activity patterns. Motivated by these two observations, we introduce a class of probabilistic models which takes into account the prior knowledge that the neural population could be globally coupled and close to critical. These models consist of an energy function which parametrizes interactions between small groups of neurons, and an arbitrary positive, strictly increasing, and twice differentiable function which maps the energy of a population pattern to its probability. We show that: 1) augmenting a pairwise Ising model with a nonlinearity yields an accurate description of the activity of retinal ganglion cells which outperforms previous models based on the summed activity of neurons; 2) prior knowledge that the population is critical translates to prior expectations about the shape of the nonlinearity; 3) the nonlinearity admits an interpretation in terms of a continuous latent variable globally coupling the system whose distribution we can infer from data. Our method is independent of the underlying system’s state space; hence, it can be applied to other systems such as natural scenes or amino acid sequences of proteins which are also known to exhibit criticality.
Highlights
IntroductionRecent progress in recording technology that permits monitoring the activity of large neural populations simultaneously has enabled us to infer detailed large-scale probabilistic models for neural activity and, to document and interpret patterns of statistical dependencies between neural responses
Most models used to date to analyze recordings from large neural populations do not take this observation explicitly into account
We aim to bridge this gap by designing probabilistic models whose structure reflects the expectation that the population is close to critical
Summary
Recent progress in recording technology that permits monitoring the activity of large neural populations simultaneously has enabled us to infer detailed large-scale probabilistic models for neural activity and, to document and interpret patterns of statistical dependencies between neural responses. The first salient feature is that neural populations are often “globally coupled.” While it has been appreciated for some time that neurons do not spike independently, the approximation that their interactions are well-described by low-order statistical dependencies (e.g., pairwise interactions) has provided powerful descriptions of the data, known as pairwise maximum entropy (Ising-like) models or, alternatively, as fully-visible Boltzmann machines [8,9,10]. For example, the population synchrony, or the summed activity over all neurons in a given time bin, represents one such global statistic that probabilistic models can reproduce, leading to the so-called “K-pairwise” models [11, 13, 14]. The increased performance of the proposed models originates in the models’ ability to capture higher-order correlations in neural spiking through a smart guess for the global (macroscopic) statistic of the population activity
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