Abstract
Pairwise maximum-entropy models have been used in neuroscience to predict the activity of neuronal populations, given only the time-averaged correlations of the neuron activities. This paper provides evidence that the pairwise model, applied to experimental recordings, would produce a bimodal distribution for the population-averaged activity, and for some population sizes the second mode would peak at high activities, that experimentally would be equivalent to 90% of the neuron population active within time-windows of few milliseconds. Several problems are connected with this bimodality: 1. The presence of the high-activity mode is unrealistic in view of observed neuronal activity and on neurobiological grounds. 2. Boltzmann learning becomes non-ergodic, hence the pairwise maximum-entropy distribution cannot be found: in fact, Boltzmann learning would produce an incorrect distribution; similarly, common variants of mean-field approximations also produce an incorrect distribution. 3. The Glauber dynamics associated with the model is unrealistically bistable and cannot be used to generate realistic surrogate data. This bimodality problem is first demonstrated for an experimental dataset from 159 neurons in the motor cortex of macaque monkey. Evidence is then provided that this problem affects typical neural recordings of population sizes of a couple of hundreds or more neurons. The cause of the bimodality problem is identified as the inability of standard maximum-entropy distributions with a uniform reference measure to model neuronal inhibition. To eliminate this problem a modified maximum-entropy model is presented, which reflects a basic effect of inhibition in the form of a simple but non-uniform reference measure. This model does not lead to unrealistic bimodalities, can be found with Boltzmann learning, and has an associated Glauber dynamics which incorporates a minimal asymmetric inhibition.
Highlights
Correlated activity between pairs of cells was observed early on in the history of neuroscience [1, 2]
The Glauber dynamics associated with the model is unrealistically bistable and cannot be used to generate realistic surrogate data
In the final “Discussion” we argue that the use of such a measure is not just an ad hoc solution, but a choice required by the underlying biology of neuronal networks: the necessity of non-uniform reference measures is well-known in other statistical scientific fields, like radioastronomy and quantum mechanics
Summary
Correlated activity between pairs of cells was observed early on in the history of neuroscience [1, 2]. Direct experimental evidence for a functional role of correlated activity is the observation that the synchronous pairwise activation of neurons significantly deviates from the uncorrelated case in tight correspondence with behaviour. Such synchronous events have been observed in motor cortex [9, 10] at time points of expected, task-relevant information. In primary visual cortex they appear in relation to saccades (eye movements) [11, 12] Another argument for the functional relevance of correlations is the robustness of signals represented by synchronous activity against noise [13]. Both these views are partly true, prompting us to find ways to distinguish functionally relevant correlated events from the uninformative background
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