Related papers: Spike train statistics and Gibbs distributions
Spiking activity in cortical networks is nonlinear in nature. The linear-nonlinear cascade model, some versions of which are also known as point-process generalized linear model, can efficiently capture the nonlinear dynamics exhibited by…
Maximum entropy models provide the least constrained probability distributions that reproduce statistical properties of experimental datasets. In this work we characterize the learning dynamics that maximizes the log-likelihood in the case…
A well-known result across information theory, machine learning, and statistical physics shows that the maximum entropy distribution under a mean constraint has an exponential form called the Gibbs-Boltzmann distribution. This is used for…
We consider a wide class of spiking neuron models, defined by rather general set of conditions typical for basic models like leaky integrate and fire, or binding neuron model. A neuron is fed with a point renewal process. A relation between…
Large-scale neuromorphic architectures consist of computing tiles that communicate spikes using a shared interconnect. The communication patterns in such systems are inherently sparse, asynchronous, and localized due to the spiking nature…
We present a hidden Markov model that describes variation in an animal's position associated with varying levels of activity in action potential spike trains of individual place cell neurons. The model incorporates a coarse-graining of…
Sampling considerations limit the experimental conditions under which information theoretic analyses of neurophysiological data yield reliable results. We develop a procedure for computing the full temporal entropy and information of…
We study the statistical properties of the stationary firing-rate states of a neural network model with quenched disorder. The model has arbitrary size, discrete-time evolution equations and binary firing rates, while the topology and the…
We consider a fully-connected network of leaky integrate-and-fire neurons with spike-timing-dependent plasticity. The plasticity is controlled by a parameter representing the expected weight of a synapse between neurons that are firing…
Generalized Linear Models (GLMs) have been used extensively in statistical models of spike train data. However, the maximum likelihood estimates of the model parameters and their uncertainty, can be challenging to compute in situations…
Perturbed by natural hazards, community-level infrastructure networks operate like many-body systems, with behaviors emerging from coupling individual component dynamics with group correlations and interactions. It follows that we can…
Although the spike-trains in neural networks are mainly constrained by the neural dynamics itself, global temporal constraints (refractoriness, time precision, propagation delays, ..) are also to be taken into account. These constraints are…
The major problem in information theoretic analysis of neural responses and other biological data is the reliable estimation of entropy--like quantities from small samples. We apply a recently introduced Bayesian entropy estimator to…
This Chapter reviews statistical models for the probability distribution of money developed in the econophysics literature since the late 1990s. In these models, economic transactions are modeled as random transfers of money between the…
Analytical expressions are put forward to investigate the forced spiking activity of abstract neuron models such as the driven leaky integrate-and-fire (LIF) model. The method is valid in a wide parameter regime beyond the restraining…
We introduce efficient algorithms for approximate sampling from symmetric Gibbs distributions on the sparse random (hyper)graph. The examples we consider include (but are not restricted to) important distributions on spin systems and…
We consider the development of hyperbolic transport models for the propagation in space of an epidemic phenomenon described by a classical compartmental dynamics. The model is based on a kinetic description at discrete velocities of the…
A model for diffusion on a cubic lattice with a random distribution of traps is developed. The traps are redistributed at certain time intervals. Such models are useful for describing systems showing dynamic disorder, such as ion-conducting…
We introduce a novel training principle for probabilistic models that is an alternative to maximum likelihood. The proposed Generative Stochastic Networks (GSN) framework is based on learning the transition operator of a Markov chain whose…
This paper introduces a class of stochastic models of interacting neurons with emergent dynamics similar to those seen in local cortical populations, and compares them to very simple reduced models driven by the same mean excitatory and…