123 research outputs found
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
State-Space Models and Latent Processes in the Statistical Analysis of Neural Data
This thesis develops and applies statistical methods for the analysis of neural data. In the second chapter we incorporate a latent process to the Generalized Linear Model framework. We develop and apply our framework to estimate the linear filters of an entire population of retinal ganglion cells while taking into account the effects of common-noise the cells might share. We are able to capture the encoding and decoding of visual stimulus to neural code. Our formalism gives us insight into the underlying architecture of the neural system. And we are able to estimate the common-noise that the cells receive. In the third chapter we discuss methods for optimally inferring the synaptic inputs to an electrotonically compact neuron, given intracellular voltage-clamp or current-clamp recordings from the postsynaptic cell. These methods are based on sequential Monte Carlo techniques ("particle filtering"). We demonstrate, on model data, that these methods can recover the time course of excitatory and inhibitory synaptic inputs accurately on a single trial. In the fourth chapter we develop a more general approach to the state-space filtering problem. Our method solves the same recursive set of Markovian filter equations as the particle filter, but we replace all importance sampling steps with a more general Markov chain Monte Carlo (MCMC) step. Our algorithm is especially well suited for problems where the model parameters might be misspecified
Training deep neural density estimators to identify mechanistic models of neural dynamics
Mechanistic modeling in neuroscience aims to explain observed phenomena in terms of underlying causes. However, determining which model parameters agree with complex and stochastic neural data presents a significant challenge. We address this challenge with a machine learning tool which uses deep neural density estimators-- trained using model simulations-- to carry out Bayesian inference and retrieve the full space of parameters compatible with raw data or selected data features. Our method is scalable in parameters and data features, and can rapidly analyze new data after initial training. We demonstrate the power and flexibility of our approach on receptive fields, ion channels, and Hodgkin-Huxley models. We also characterize the space of circuit configurations giving rise to rhythmic activity in the crustacean stomatogastric ganglion, and use these results to derive hypotheses for underlying compensation mechanisms. Our approach will help close the gap between data-driven and theory-driven models of neural dynamics
Sequential estimation of neural models by Bayesian filtering
Un dels reptes més difÃcils de la neurociència és el d'entendre la connectivitat del cervell. Aquest problema es pot tractar des de diverses perspectives, aquà ens centrem en els fenòmens locals que ocorren en una sola neurona. L'objectiu final és, doncs, entendre la dinà mica de les neurones i com la interconnexió amb altres neurones afecta al seu estat. Les observacions de traces del potencial de membrana constitueixen la principal font d'informació per a derivar models matemà tics d'una neurona, amb cert sentit biofÃsic. En particular, la dinà mica de les variables auxiliars i els parà metres del model són estimats a partir d'aquestes traces de voltatge. El procés és en general costós i tÃpicament implica una gran varietat de blocatges quÃmics de canals iònics, aixà com una certa incertesa en els valors dels parà metres a causa del soroll de mesura. D'altra banda, les traces de potencial de membrana també són útils per obtenir informació valuosa sobre l'entrada sinà ptica, un problema invers sense solució satisfactòria a hores d'ara. En aquesta Tesi, estem interessats en mètodes d'estimació seqüencial, que permetin evitar la necessitat de repeticions que podrien ser contaminades per la variabilitat neuronal. En particular, ens concentrem en mètodes per extreure l'activitat intrÃnseca dels canals iònics, és a dir, les probabilitats d'obertura i tancament de canals iònics, i la contribució de les conductà ncies sinà ptiques. Hem dissenyat un mètode basat en la teoria Bayesiana de filtrat per inferir seqüencialment aquestes quantitats a partir d'una única traça de voltatge, potencialment sorollosa. El mètode d'estimació proposat està basat en la suposició d'un model de neurona conegut. Això és cert fins a cert punt, però la majoria dels parà metres en el model han de ser estimats per endavant (això és valid per a qualsevol model). Per tant, el mètode s'ha millorat pel cas de models amb parà metres desconeguts, incloent-hi un procediment per estimar conjuntament els parà metres i les variables dinà miques. Hem validat els mètodes d'inferència proposats mitjançant simulacions realistes. Les prestacions en termes d'error d'estimació s'han comparat amb el lÃmit teòric, que s'ha derivat també en el marc d'aquesta Tesi
Estimation of synaptic conductances in presence of nonlinear effects caused by subthreshold ionic currents
Subthreshold fluctuations in neuronal membrane potential traces contain nonlinear
components, and employing nonlinear models might improve the statistical inference. We propose a new strategy to estimate synaptic conductances, which has been tested using in silico data and applied to in vivo recordings. The model is constructed to capture the nonlinearities caused by subthreshold activated currents, and the estimation procedure can discern between excitatory and inhibitory conductances using only one membrane potential trace. More precisely, we perform second order approximations of biophysical models to capture the subthreshold nonlinearities, resulting in quadratic integrate-and-fire models, and apply approximate maximum likelihood estimation where we only suppose that conductances are stationary in a 50–100 ms time window. The results show an improvement compared to existent procedures for the models tested here.Peer ReviewedPostprint (published version
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