Maximum Entropy Approaches to Living Neural Networks (original) (raw)
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A Maximum Entropy Model Applied to Temporal Correlations in Cortical Networks
Bulletin of the American Physical Society, 2008
Multi-neuron firing states are often observed, yet are predicted to be rare by models that assume independent firing. To predict these states, two groups recently applied a second-order maximum entropy model that used only observed firing rates and pairwise interactions as parameters (Schneidman et al., 2006; Shlens et al., 2006). Interestingly, these models predicted 90-99 {\%} of network correlations. If generally applicable, this approach could vastly simplify analyses of complex networks. However, this work did not address the ...
Physical Review E
Maximum Entropy models can be inferred from large data-sets to uncover how collective dynamics emerge from local interactions. Here, such models are employed to investigate neurons recorded by multielectrode arrays in the human and monkey cortex. Taking advantage of the separation of excitatory and inhibitory neuron types, we construct a model including this distinction. This approach allows to shed light upon differences between excitatory and inhibitory activity across different brain states such as wakefulness and deep sleep, in agreement with previous findings. Additionally, Maximum Entropy models can also unveil novel features of neuronal interactions, which are found to be dominated by pairwise interactions during wakefulness, but are population-wide during deep sleep. In particular, inhibitory neurons are observed to be strongly tuned to the inhibitory population. Overall, we demonstrate Maximum Entropy models can be useful to analyze data-sets with classified neuron types, and to reveal the respective roles of excitatory and inhibitory neurons in organizing coherent dynamics in the cerebral cortex.
2010
Simultaneously recorded neurons exhibit correlations whose underlying causes are not known. Here, we use a population of threshold neurons receiving correlated inputs to model neural population recordings. We show analytically that small changes in second-order correlations can lead to large changes in higher correlations, and that these higher-order correlations have a strong impact on the entropy, sparsity and statistical heat capacity of the population. Remarkably, our findings for this simple model may explain a couple of surprising effects recently observed in neural population recordings.
A Maximum Entropy Model Applied to Spatial and Temporal Correlations from Cortical Networks In Vitro
Journal of Neuroscience, 2008
Multineuron firing patterns are often observed, yet are predicted to be rare by models that assume independent firing. To explain these correlated network states, two groups recently applied a second-order maximum entropy model that used only observed firing rates and pairwise interactions as parameters (Schneidman et al., 2006; Shlens et al., 2006). Interestingly, with these minimal assumptions they predicted 90-99% of network correlations. If generally applicable, this approach could vastly simplify analyses of complex networks. However, this initial work was done largely on retinal tissue, and its applicability to cortical circuits is mostly unknown. This work also did not address the temporal evolution of correlated states. To investigate these issues, we applied the model to multielectrode data containing spontaneous spikes or local field potentials from cortical slices and cultures. The model worked slightly less well in cortex than in retina, accounting for 88 Ϯ 7% (mean Ϯ SD) of network correlations. In addition, in 8 of 13 preparations, the observed sequences of correlated states were significantly longer than predicted by concatenating states from the model. This suggested that temporal dependencies are a common feature of cortical network activity, and should be considered in future models. We found a significant relationship between strong pairwise temporal correlations and observed sequence length, suggesting that pairwise temporal correlations may allow the model to be extended into the temporal domain. We conclude that although a second-order maximum entropy model successfully predicts correlated states in cortical networks, it should be extended to account for temporal correlations observed between states.
Higher-Order Statistics of Input Ensembles and the Response of Simple Model Neurons
Neural Computation, 2003
Pairwise correlations among spike trains recorded in vivo have been frequently reported. It has been argued that correlated activity could play an important role in the brain, because it efficiently modulates the response of a postsynaptic neuron. We show here that a neuron's output firing rate critically depends on the higher-order statistics of the input ensemble. We constructed two statistical models of populations of spiking neurons that fired with the same rates and had identical pairwise correlations, but differed with regard to the higher-order interactions within the population. The first ensemble was characterized by clusters of spikes synchronized over the whole population. In the second ensemble, the size of spike clusters was, on average, proportional to the pairwise correlation. For both input models, we assessed the role of the size of the population, the firing rate, and the pairwise correlation on the output rate of two simple model neurons: a continuous firing-rate model and a conductance-based leaky integrate-and-fire neuron. An approximation to the mean output rate of the firing-rate neuron could be derived analytically with the help of shot noise theory. Interestingly, the essential features of the mean response of the two neuron models were similar. For both neuron models, the three input parameters played radically different roles with respect to the postsynaptic firing rate, depending on the interaction structure of the input. For instance, in the case of an ensemble with small and distributed spike clusters, the output firing rate was efficiently controlled by the size of the input population. In addition to the interaction structure, the ratio of inhibition to excitation was found to strongly modulate the effect of correlation on the postsynaptic firing rate.
Maximum-entropy and representative samples of neuronal activity: a dilemma
The present work shows that the maximum-entropy method can be applied to a sample of neuronal recordings along two different routes: (1) apply to the sample; or (2) apply to a larger, unsampled neuronal population from which the sample is drawn, and then marginalize to the sample. These two routes give inequivalent results. The second route can be further generalized to the case where the size of the larger population is unknown. Which route should be chosen? Some arguments are presented in favour of the second. This work also presents and discusses probability formulae that relate states of knowledge about a population and its samples, and that may be useful for sampling problems in neuroscience.
Modeling neural activity at the ensemble level
Cornell University - arXiv, 2015
Here we demonstrate that the activity of neural ensembles can be quantitatively modeled. We first show that an ensemble dynamical model (EDM) accurately approximates the distribution of voltages and average firing rate per neuron of a population of simulated integrate-and-fire neurons. EDMs are high-dimensional nonlinear dynamical models. To faciliate the estimation of their parameters we present a dimensionality reduction method and study its performance with simulated data. We then introduce and evaluate a maximum-likelihood method to estimate connectivity parameters in networks of EDMS. Finally, we show that this model an methods accurately approximate the high-gamma power evoked by pure tones in the auditory cortex of rodents. Overall, this article demonstrates that quantitatively modeling brain activity at the ensemble level is indeed possible, and opens the way to understanding the computations performed by neural ensembles, which could revolutionarize our understanding of brain function.
Redundancy and synergy arising from pairwise correlations in neuronal ensembles
Journal of computational neuroscience
Multielectrode arrays allow recording of the activity of many single neurons, from which correlations can be calculated. The functional roles of correlations can be revealed by measures of the information conveyed by neuronal activity; a simple formula has been shown to discriminate the information transmitted by individual spikes from the positive or negative contributions due to correlations (Panzeri et al., 1999). Here, this analysis, previously applied to recordings from small ensembles, is developed further by considering a model of a large ensemble, in which correlations among the signal and noise components of neuronal firing are small in absolute value and entirely random in origin. Even such small random correlations are shown to lead to large possible synergy or redundancy, whenever the time window for extracting information from neuronal firing extends to the order of the mean interspike interval. In addition, a sample of recordings from rat barrel cortex illustrates the ...
Exact computation of the maximum-entropy potential of spiking neural-network models
Physical Review E, 2014
Understanding how stimuli and synaptic connectivity influence the statistics of spike patterns in neural networks is a central question in computational neuroscience. Maximum Entropy approach has been successfully used to characterize the statistical response of simultaneously recorded spiking neurons responding to stimuli. But, in spite of good performance in terms of prediction, the fitting parameters do not explain the underlying mechanistic causes of the observed correlations. On the other hand, mathematical models of spiking neurons (neuro-mimetic models) provide a probabilistic mapping between stimulus, network architecture and spike patterns in terms of conditional probabilities. In this paper we build an exact analytical mapping between neuro-mimetic and Maximum Entropy models.