Generalized Linear Models for Point Process Analyses of Neural Spiking Activity

2015 ◽  
pp. 1284-1287
Author(s):  
Zhe Chen ◽  
Emery N. Brown
Keyword(s):  
Point Process ◽  
Generalized Linear Models ◽  
Linear Models ◽  
Neural Spiking ◽  
Spiking Activity

Estimating a State-Space Model from Point Process Observations

2003 ◽  
Vol 15 (5) ◽  
pp. 965-991 ◽  
Author(s):  
Anne C. Smith ◽  
Emery N. Brown
Keyword(s):  
State Space ◽  
Point Process ◽  
State Space Model ◽  
The State ◽  
Conditional Intensity ◽  
Space Model ◽  
Neural Spiking ◽  
Latent Process ◽  
Conditional Intensity Function ◽  
Spiking Activity

A widely used signal processing paradigm is the state-space model. The state-space model is defined by two equations: an observation equation that describes how the hidden state or latent process is observed and a state equation that defines the evolution of the process through time. Inspired by neurophysiology experiments in which neural spiking activity is induced by an implicit (latent) stimulus, we develop an algorithm to estimate a state-space model observed through point process measurements. We represent the latent process modulating the neural spiking activity as a gaussian autoregressive model driven by an external stimulus. Given the latent process, neural spiking activity is characterized as a general point process defined by its conditional intensity function. We develop an approximate expectation-maximization (EM) algorithm to estimate the unobservable state-space process, its parameters, and the parameters of the point process. The EM algorithm combines a point process recursive nonlinear filter algorithm, the fixed interval smoothing algorithm, and the state-space covariance algorithm to compute the complete data log likelihood efficiently. We use a Kolmogorov-Smirnov test based on the time-rescaling theorem to evaluate agreement between the model and point process data. We illustrate the model with two simulated data examples: an ensemble of Poisson neurons driven by a common stimulus and a single neuron whose conditional intensity function is approximated as a local Bernoulli process.

scholarly journals Efficient Spline Regression for Neural Spiking Data

2020 ◽  
Author(s):  
Mehrad Sarmashghi ◽  
Shantanu P Jadhav ◽  
Uri Eden
Keyword(s):  
Spike Train ◽  
Point Process ◽  
Statistical Power ◽  
Linear Models ◽  
Basis Functions ◽  
Ca1 Region ◽  
Neural Spiking ◽  
Spline Basis ◽  
Cardinal Splines ◽  
The Relationship

AbstractPoint process generalized linear models (GLMs) provide a powerful tool for characterizing the coding properties of neural populations. Spline basis functions are often used in point process GLMs, when the relationship between the spiking and driving signals are nonlinear, but common choices for the structure of these spline bases often lead to loss of statistical power and numerical instability when the signals that influence spiking are bounded above or below. In particular, history dependent spike train models often suffer these issues at times immediately following a previous spike. This can make inferences related to refractoriness and bursting activity more challenging. Here, we propose a modified set of spline basis functions that assumes a flat derivative at the endpoints and show that this limits the uncertainty and numerical issues associated with cardinal splines. We illustrate the application of this modified basis to the problem of simultaneously estimating the place field and history dependent properties of a set of neurons from the CA1 region of rat hippocampus, and compare it with the other commonly used basis functions. We have made code available in MATLAB to implement spike train regression using these modified basis functions.

scholarly journals Forecasting Seizure Risk over Days

2019 ◽  
Author(s):  
Timothée Proix ◽  
Wilson Truccolo ◽  
Marc G. Leguia ◽  
David King-Stephens ◽  
Vikram R. Rao ◽  
...  
Keyword(s):  
Risk Stratification ◽  
Point Process ◽  
Generalized Linear Models ◽  
Linear Models ◽  
Brain Activity ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Preventative Interventions ◽  
Intracranial Electroencephalography ◽  
Personalized Risk

AbstractFor persons with epilepsy, much suffering stems from the apparent unpredictability of seizures. Historically, efforts to predict seizures have sought to detect changes in brain activity in the seconds to minutes preceding seizures (pre-ictal period), a timeframe that limits preventative interventions. Recently, converging evidence from studies using chronic intracranial electroencephalography revealed that brain activity in epilepsy has a robust cyclical structure over hours (circadian) and days (multidien). These cycles organize pro-ictal states, hours-to days-long periods of heightened seizure risk, raising the possibility of forecasting seizures over horizons longer than the pre-ictal period. Here, using cEEG from 18 subjects, we developed point-process generalized linear models incorporating cyclical variables at multiple time-scales to show that seizure risk can be forecasted accurately over days in most subjects. Personalized risk-stratification days in advance of seizures is unprecedented and may enable novel preventative strategies.

scholarly journals Efficient spline regression for neural spiking data

PLoS ONE ◽  
2021 ◽  
Vol 16 (10) ◽  
pp. e0258321
Author(s):  
Mehrad Sarmashghi ◽  
Shantanu P. Jadhav ◽  
Uri Eden
Keyword(s):  
Spike Train ◽  
Point Process ◽  
Statistical Power ◽  
Linear Models ◽  
Basis Functions ◽  
Ca1 Region ◽  
Neural Spiking ◽  
Spline Basis ◽  
Cardinal Splines ◽  
The Relationship

Point process generalized linear models (GLMs) provide a powerful tool for characterizing the coding properties of neural populations. Spline basis functions are often used in point process GLMs, when the relationship between the spiking and driving signals are nonlinear, but common choices for the structure of these spline bases often lead to loss of statistical power and numerical instability when the signals that influence spiking are bounded above or below. In particular, history dependent spike train models often suffer these issues at times immediately following a previous spike. This can make inferences related to refractoriness and bursting activity more challenging. Here, we propose a modified set of spline basis functions that assumes a flat derivative at the endpoints and show that this limits the uncertainty and numerical issues associated with cardinal splines. We illustrate the application of this modified basis to the problem of simultaneously estimating the place field and history dependent properties of a set of neurons from the CA1 region of rat hippocampus, and compare it with the other commonly used basis functions. We have made code available in MATLAB to implement spike train regression using these modified basis functions.

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