Spatio-temporal spike train analysis for large scale networks using the maximum entropy principle and Monte Carlo method

Nasser, Hassan; Marre, Olivier; Cessac, Bruno

doi:10.1088/1742-5468/2013/03/p03006

Cited by 31 publications

(46 citation statements)

References 84 publications

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“…First, low-order MEP analysis is often insufficient to accurately reconstruct the probability distribution of network states in synchronized networks since the high-order effective interactions in such cases are often not small [36]. Second, as both the order of moment constraints and the network size, n, increase, the existing algorithms to estimate effective interactions for a large network become very slow [19,26]. Because the number all network states, i.e., 2 n , is too large when n is a large number, the existing algorithms estimate moments of the MEP distribution using Monte Carlo sampling or its variants from the MEP distribution, which are often very slow when the dimension of the distribution is high [19,26].…”

Section: Discussionmentioning

confidence: 99%

Maximum entropy principle analysis in network systems with short-time recordings

Crodelle

Zhou

et al. 2019

Phys. Rev. E

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In many realistic systems, maximum entropy principle (MEP) analysis provides an effective characterization of the probability distribution of network states. However, to implement the MEP analysis, a sufficiently long-time data recording in general is often required, e.g., hours of spiking recordings of neurons in neuronal networks. The issue of whether the MEP analysis can be successfully applied to network systems with data from short recordings has yet to be fully addressed. In this work, we investigate relationships underlying the probability distributions, moments, and effective interactions in the MEP analysis and then show that, with short recordings of network dynamics, the MEP analysis can be applied to reconstructing probability distributions of network states under the condition of asynchronous activity of nodes in the network. Using spike trains obtained from both Hodgkin-Huxley neuronal networks and electrophysiological experiments, we verify our results and demonstrate that MEP analysis provides a tool to investigate the neuronal population coding properties, even for short recordings.

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Section: Discussionmentioning

confidence: 99%

Maximum entropy principle analysis in network systems with short-time recordings

Crodelle

Zhou

et al. 2019

Phys. Rev. E

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“…3A). To study these trajectories, we extended the pairwise maximum entropy models by adding temporal correlations between units [41,42]. To model a sequence of states,…”

Section: Temporal Dependence and Transition Rules Between Population mentioning

confidence: 99%

Strongly correlated spatiotemporal encoding and simple decoding in the prefrontal cortex

Karpas

Maoz

Kiani

et al. 2019

Preprint

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We studied the fine temporal structure of spiking patterns of groups of up to 100 simultaneously recorded units in the prefrontal cortex of monkeys performing a visual discrimination task. We characterized the vocabulary of population activity patterns using 10 ms time bins and found that different sets of population activity patterns (codebooks) are used in different task epochs and that spiking correlations between units play a large role in defining those codebooks. Models that ignore those correlations fail to capture the population codebooks in all task epochs. Further, we show that temporal sequences of population activity patterns have strong history-dependence and are governed by different transition probabilities between patterns and different correlation time scales, in the different task epochs, suggesting different computational dynamics governing each epoch. Together, the large impact of spatial and temporal correlations on the dynamics of the population code makes the observed sequences of activity patterns many orders of magnitude more likely to appear than predicted by models that ignore these correlations and rely only on the population rates. Surprisingly, however, models that ignore these correlations perform quite well for decoding behavior from population responses. The difference of encoding and decoding complexity of the neural codebook suggests that one of the goals of the complex encoding scheme in the prefrontal cortex is to accommodate simple decoders that do not have to learn correlations.

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“…Another popular statistical model for characterizing population spike trains is the maximum entropy (MaxEnt) model with a log-linear form [16, 17]. Given an ensemble of C neurons, the ensemble spike activity can be characterized by the following form:

\begin{matrix} p (X) = \frac{1}{𝒵 (X)} \exp (\sum_{i = normal1}^{C} θ_{c} 〈 x_{c} 〉 + \sum_{i, j}^{C} θ_{i j} 〈 x_{i} x_{j} 〉) \\ \equiv \frac{1}{𝒵 (X)} \exp (\sum_{i = normal1}^{C + C^{normal2}} θ_{i} f_{i} (X)), \end{matrix}

where x i ∈ {−1, +1}, 〈·〉 denotes the sample average, 〈 x c 〉 denotes the mean firing rate of the c th neuron, f i ( X ) denotes a generic function of X (where the couplings θ i have to match the measured expectation values 〈 f i ( X )〉), and 𝒵 ( X ) denotes the partition function.…”

Section: Introductionmentioning

confidence: 99%

An Overview of Bayesian Methods for Neural Spike Train Analysis

Chen

2013

Computational Intelligence and Neuroscience

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Neural spike train analysis is an important task in computational neuroscience which aims to understand neural mechanisms and gain insights into neural circuits. With the advancement of multielectrode recording and imaging technologies, it has become increasingly demanding to develop statistical tools for analyzing large neuronal ensemble spike activity. Here we present a tutorial overview of Bayesian methods and their representative applications in neural spike train analysis, at both single neuron and population levels. On the theoretical side, we focus on various approximate Bayesian inference techniques as applied to latent state and parameter estimation. On the application side, the topics include spike sorting, tuning curve estimation, neural encoding and decoding, deconvolution of spike trains from calcium imaging signals, and inference of neuronal functional connectivity and synchrony. Some research challenges and opportunities for neural spike train analysis are discussed.

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Spatio-temporal spike train analysis for large scale networks using the maximum entropy principle and Monte Carlo method

Cited by 31 publications

References 84 publications

Maximum entropy principle analysis in network systems with short-time recordings

Maximum entropy principle analysis in network systems with short-time recordings

Strongly correlated spatiotemporal encoding and simple decoding in the prefrontal cortex

An Overview of Bayesian Methods for Neural Spike Train Analysis

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