Related papers: Spike train statistics and Gibbs distributions
Dependency networks (Heckerman et al., 2000) are potential probabilistic graphical models for systems comprising a large number of variables. Like Bayesian networks, the structure of a dependency network is represented by a directed graph,…
Spiking neural networks (SNNs) are distributed trainable systems whose computing elements, or neurons, are characterized by internal analog dynamics and by digital and sparse synaptic communications. The sparsity of the synaptic spiking…
Learning is based on synaptic plasticity, which affects and is driven by neural activity. Because pre- and postsynaptic spiking activity is shaped by randomness, the synaptic weights follow a stochastic process, requiring a probabilistic…
Neurons perform computations, and convey the results of those computations through the statistical structure of their output spike trains. Here we present a practical method, grounded in the information-theoretic analysis of prediction, for…
Understanding how stimuli and synaptic connectivity in uence 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…
Advances in neuroscience have enabled researchers to measure the activities of large numbers of neurons simultaneously in behaving animals. We have access to the fluorescence of each of the neurons which provides a first-order approximation…
We use statistical estimates of the entropy rate of spike train data in order to make inferences about the underlying structure of the spike train itself. We first examine a number of different parametric and nonparametric estimators (some…
We derive a synaptic weight update rule for learning temporally precise spike train to spike train transformations in multilayer feedforward networks of spiking neurons. The framework, aimed at seamlessly generalizing error backpropagation…
The nervous system represents time-dependent signals in sequences of discrete action potentials or spikes, all spikes are identical so that information is carried only in the spike arrival times. We show how to quantify this information, in…
We study in this paper the effect of an unique initial stimulation on random recurrent networks of leaky integrate and fire neurons. Indeed given a stochastic connectivity this so-called spontaneous mode exhibits various non trivial…
Increasing availability and quality of actual, as opposed to scheduled, open transport data offers new possibilities for capturing the spatiotemporal dynamics of the railway and other networks of social infrastructure. One way to describe…
Stochastic differential equations provide a powerful tool for modelling dynamic phenomena affected by random noise. In case of repeated observations of time series for several experimental units, it is often the case that some of the…
Statistical properties of spike trains measured from a sensory neuron in-vivo are studied experimentally and theoretically. Experiments are performed on an identified neuron in the visual system of the blowfly. It is shown that the spike…
We review two examples where the linear response of a neuronal network submitted to an external stimulus can be derived explicitely, including network parameters dependence. This is done in a statistical physics-like approach where one…
Replicated network data are increasingly available in many research fields. In connectomic applications, inter-connections among brain regions are collected for each patient under study, motivating statistical models which can flexibly…
We consider Gibbs and block Gibbs samplers for a Bayesian hierarchical version of the one-way random effects model. Drift and minorization conditions are established for the underlying Markov chains. The drift and minorization are used in…
Spiking Neural Networks (SNNs) are distributed trainable systems whose computing elements, or neurons, are characterized by internal analog dynamics and by digital and sparse synaptic communications. The sparsity of the synaptic spiking…
In this work we study the entropy of the Gibbs state corresponding to a graph. The Gibbs state is obtained from the Laplacian, normalized Laplacian or adjacency matrices associated with a graph. We calculated the entropy of the Gibbs state…
The dynamics of network formation are generally very complex, making the study of distributions over the space of networks often intractable. Under a condition called conservativeness, I show that the stationary distribution of a network…
The seemingly stochastic transient dynamics of neocortical circuits observed in vivo have been hypothesized to represent a signature of ongoing stochastic inference. In vitro neurons, on the other hand, exhibit a highly deterministic…