Extracting state transition dynamics from multiple spike trains using hidden Markov models with correlated poisson...

Area of Science:

• Computational Neuroscience
• Statistical Modeling
• Time Series Analysis

Background:

• Neural activity is dynamic and nonstationary, requiring models that capture temporal variations.
• Traditional Hidden Markov Models (HMMs) with independent Poisson outputs struggle to represent changing neural correlations.
• Modulating firing rates alone is insufficient for tracking correlation changes in neural data.

Purpose of the Study:

• To develop an advanced Hidden Markov Model (HMM) capable of tracking dynamic neural correlations.
• To incorporate correlation terms into the HMM output distribution using a multivariate Poisson model.
• To address the limitations of existing models in representing complex neural activity patterns.

Main Methods:

• Applied a multivariate Poisson distribution with correlation terms as the output layer for HMMs.
• Formulated a variational Bayes (VB) inference method for parameter estimation and model selection.
• Developed an efficient algorithm utilizing the recursive properties of the multivariate Poisson distribution for posterior computation.

Main Results:

• The variational Bayes approach automatically determined the optimal number of hidden states and correlation types.
• The proposed model successfully avoided the overlearning problem in neural data analysis.
• Demonstrated effective performance on both synthetic datasets and real songbird neural recordings.

Conclusions:

• The multivariate Poisson HMM provides a powerful framework for analyzing nonstationary neural data with time-varying correlations.
• This method offers improved accuracy in modeling neural dynamics compared to traditional HMMs.
• The developed VB inference and efficient algorithm facilitate robust analysis of complex neural spike trains.