713 research outputs found
Spike train statistics and Gibbs distributions
This paper is based on a lecture given in the LACONEU summer school,
Valparaiso, January 2012. We introduce Gibbs distribution in a general setting,
including non stationary dynamics, and present then three examples of such
Gibbs distributions, in the context of neural networks spike train statistics:
(i) Maximum entropy model with spatio-temporal constraints; (ii) Generalized
Linear Models; (iii) Conductance based Inte- grate and Fire model with chemical
synapses and gap junctions.Comment: 23 pages, submitte
Entropy-based parametric estimation of spike train statistics
We consider the evolution of a network of neurons, focusing on the asymptotic
behavior of spikes dynamics instead of membrane potential dynamics. The spike
response is not sought as a deterministic response in this context, but as a
conditional probability : "Reading out the code" consists of inferring such a
probability. This probability is computed from empirical raster plots, by using
the framework of thermodynamic formalism in ergodic theory. This gives us a
parametric statistical model where the probability has the form of a Gibbs
distribution. In this respect, this approach generalizes the seminal and
profound work of Schneidman and collaborators. A minimal presentation of the
formalism is reviewed here, while a general algorithmic estimation method is
proposed yielding fast convergent implementations. It is also made explicit how
several spike observables (entropy, rate, synchronizations, correlations) are
given in closed-form from the parametric estimation. This paradigm does not
only allow us to estimate the spike statistics, given a design choice, but also
to compare different models, thus answering comparative questions about the
neural code such as : "are correlations (or time synchrony or a given set of
spike patterns, ..) significant with respect to rate coding only ?" A numerical
validation of the method is proposed and the perspectives regarding spike-train
code analysis are also discussed.Comment: 37 pages, 8 figures, submitte
A Bayesian approach for inferring neuronal connectivity from calcium fluorescent imaging data
Deducing the structure of neural circuits is one of the central problems of
modern neuroscience. Recently-introduced calcium fluorescent imaging methods
permit experimentalists to observe network activity in large populations of
neurons, but these techniques provide only indirect observations of neural
spike trains, with limited time resolution and signal quality. In this work we
present a Bayesian approach for inferring neural circuitry given this type of
imaging data. We model the network activity in terms of a collection of coupled
hidden Markov chains, with each chain corresponding to a single neuron in the
network and the coupling between the chains reflecting the network's
connectivity matrix. We derive a Monte Carlo Expectation--Maximization
algorithm for fitting the model parameters; to obtain the sufficient statistics
in a computationally-efficient manner, we introduce a specialized
blockwise-Gibbs algorithm for sampling from the joint activity of all observed
neurons given the observed fluorescence data. We perform large-scale
simulations of randomly connected neuronal networks with biophysically
realistic parameters and find that the proposed methods can accurately infer
the connectivity in these networks given reasonable experimental and
computational constraints. In addition, the estimation accuracy may be improved
significantly by incorporating prior knowledge about the sparseness of
connectivity in the network, via standard L penalization methods.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS303 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Detecting and Estimating Signals over Noisy and Unreliable Synapses: Information-Theoretic Analysis
The temporal precision with which neurons respond to synaptic inputs has a direct bearing on the nature of the neural code. A characterization of the neuronal noise sources associated with different sub-cellular components (synapse, dendrite, soma, axon, and so on) is needed to understand the relationship between noise and information transfer. Here we study the effect of the unreliable, probabilistic nature of synaptic transmission on information transfer in the absence of interaction among presynaptic inputs. We derive theoretical lower bounds on the capacity of a simple model of a cortical synapse under two different paradigms. In signal estimation, the signal is assumed to be encoded in the mean firing rate of the presynaptic neuron, and the objective is to estimate the continuous input signal from the postsynaptic voltage. In signal detection, the input is binary, and the presence or absence of a presynaptic action potential is to be detected from the postsynaptic voltage. The efficacy of information transfer in synaptic transmission is characterized by deriving optimal strategies under these two paradigms. On the basis of parameter values derived from neocortex, we find that single cortical synapses cannot transmit information reliably, but redundancy obtained using a small number of multiple synapses leads to a significant improvement in the information capacity of synaptic transmission
Mesoscopic modeling of hidden spiking neurons
Can we use spiking neural networks (SNN) as generative models of multi-neuronal recordings, while taking into account that most neurons are unobserved? Modeling the unobserved neurons with large pools of hidden spiking neurons leads to severely underconstrained problems that are hard to tackle with maximum likelihood estimation. In this work, we use coarse-graining and mean-field approximations to derive a bottom-up, neuronally-grounded latent variable model (neuLVM), where the activity of the unobserved neurons is reduced to a low-dimensional mesoscopic description. In contrast to previous latent variable models, neuLVM can be explicitly mapped to a recurrent, multi-population SNN, giving it a transparent biological interpretation. We show, on synthetic spike trains, that a few observed neurons are sufficient for neuLVM to perform efficient model inversion of large SNNs, in the sense that it can recover connectivity parameters, infer single-trial latent population activity, reproduce ongoing metastable dynamics, and generalize when subjected to perturbations mimicking optogenetic stimulation
A Point-process Response Model for Spike Trains from Single Neurons in Neural Circuits under Optogenetic Stimulation
Optogenetics is a new tool to study neuronal circuits that have been
genetically modified to allow stimulation by flashes of light. We study
recordings from single neurons within neural circuits under optogenetic
stimulation. The data from these experiments present a statistical challenge of
modeling a high frequency point process (neuronal spikes) while the input is
another high frequency point process (light flashes). We further develop a
generalized linear model approach to model the relationships between two point
processes, employing additive point-process response functions. The resulting
model, Point-process Responses for Optogenetics (PRO), provides explicit
nonlinear transformations to link the input point process with the output one.
Such response functions may provide important and interpretable scientific
insights into the properties of the biophysical process that governs neural
spiking in response to optogenetic stimulation. We validate and compare the PRO
model using a real dataset and simulations, and our model yields a superior
area-under-the- curve value as high as 93% for predicting every future spike.
For our experiment on the recurrent layer V circuit in the prefrontal cortex,
the PRO model provides evidence that neurons integrate their inputs in a
sophisticated manner. Another use of the model is that it enables understanding
how neural circuits are altered under various disease conditions and/or
experimental conditions by comparing the PRO parameters.Comment: 24 pages, 7 figures. R package pro implementing the proposed method
is available on CRAN at https://CRAN.R-project.org/package=pro . Published by
Statistics in Medicine at
http://onlinelibrary.wiley.com/doi/10.1002/sim.6742/ful
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