• Corpus ID: 12812368

Network Modeling of Short Over-Dispersed Spike-Counts: A Hierarchical Parametric Empirical Bayes Framework

  title={Network Modeling of Short Over-Dispersed Spike-Counts: A Hierarchical Parametric Empirical Bayes Framework},
  author={Qi She and Beth Jelfs and Rosa H.M.Chan},
  journal={arXiv: Quantitative Methods},
Accurate statistical models of neural spike responses can characterize the information carried by neural populations. Yet, challenges in recording at the level of individual neurons commonly results in relatively limited samples of spike counts, which can lead to model overfitting. Moreover, current models assume spike counts to be Poisson-distributed, which ignores the fact that many neurons demonstrate over-dispersed spiking behavior. The Negative Binomial Generalized Linear Model (NB-GLM… 


Fully Bayesian inference for neural models with negative-binomial spiking
A powerful data-augmentation framework for fully Bayesian inference in neural models with negative-binomial spiking that substantially outperforms Poisson regression on held-out data, and reveals latent structure underlying spike count correlations in simultaneously recorded spike trains.
Flexible models for spike count data with both over- and under- dispersion
It is found that COM-Poisson models with group/observation-level dispersion, where spike count variability is a function of time or stimulus, produce more accurate descriptions of spike counts compared to Poisson models as well as negative-binomial models often used as alternatives.
High-dimensional neural spike train analysis with generalized count linear dynamical systems
The generalized count linear dynamical system is developed, which relaxes the Poisson assumption by using a more general exponential family for count data and can be tractably learned by extending recent advances in variational inference techniques.
Statistical Inference for Assessing Functional Connectivity of Neuronal Ensembles With Sparse Spiking Data
The present studies compares the performance of different statistical inference procedures when applied to the estimation of functional connectivity in neuronal assemblies with sparse spiking data and found the hierarchical Bayesian approach performed favorably when compared with the other algorithms.
Empirical models of spiking in neural populations
This work argues that in the cortex, where firing exhibits extensive correlations in both time and space and where a typical sample of neurons still reflects only a very small fraction of the local population, the most appropriate model captures shared variability by a low-dimensional latent process evolving with smooth dynamics, rather than by putative direct coupling.
Maximum Likelihood Estimation of a Stochastic Integrate-and-Fire Neural Model
This work analyzes the estimation of a model of stimulus-driven neural activity in which some linear filtering process is followed by a nonlinear, probabilistic spiking stage, and forms an algorithm that is guaranteed to find the global optimum with reasonable speed.
Maximum Likelihood Estimation of a Stochastic Integrate-and-Fire Neural Encoding Model
It is proved that the log-likelihood function is concave and thus has an essentially unique global maximum that can be found using gradient ascent techniques.
Analyzing Functional Connectivity Using a Network Likelihood Model of Ensemble Neural Spiking Activity
A discrete-time version of Chornoboy, Schramm, and Karr's maximum likelihood method for the simultaneous analysis of multiple pair-wise interactions among an ensemble of neurons is devised that includes a new, efficient computational strategy, a principled method to compute starting values, and a principled stopping criterion.
A point process framework for relating neural spiking activity to spiking history, neural ensemble, and extrinsic covariate effects.
A statistical framework based on the point process likelihood function to relate a neuron's spiking probability to three typical covariates: the neuron's own spiking history, concurrent ensemble activity, and extrinsic covariates such as stimuli or behavior.
Maximum likelihood estimation of cascade point-process neural encoding models
This work investigates the shape of the likelihood function for this type of model, gives a simple condition on the nonlinearity ensuring that no non-global local maxima exist in the likelihood—leading to efficient algorithms for the computation of the maximum likelihood estimator—and discusses the implications for the form of the allowed nonlinearities.