Bayesian inference for generalized linear models for spiking neurons.

Area of Science:

• Computational Neuroscience
• Statistical Modeling

Background:

• Generalized Linear Models (GLMs) are standard for analyzing neural population activity.
• High-dimensional parameter spaces in GLMs necessitate strong regularization to prevent overfitting.
• Bayesian inference offers a principled method for regularization through informative priors.

Purpose of the Study:

• To approximate the posterior distribution of GLM parameters using Gaussian approximation via Expectation Propagation.
• To obtain posterior means and covariances for calculating Bayesian confidence intervals.
• To compare different inference techniques, including posterior mean versus maximum a posteriori estimates.

Main Methods:

• Employing the Expectation Propagation algorithm to approximate the posterior distribution of GLM parameters.
• Utilizing Bayesian inference with carefully selected priors for regularization.
• Systematic comparison of inference methods on simulated and real neural data (retinal ganglion cells).

Main Results:

• Expectation Propagation successfully approximates the posterior distribution with a Gaussian.
• The method yields estimates of the posterior mean and covariance, enabling uncertainty quantification.
• A Laplace prior combined with the posterior mean estimate demonstrated strong performance.

Conclusions:

• Expectation Propagation provides an effective Bayesian approach for regularizing GLMs in neuroscience.
• The method allows for robust parameter estimation and uncertainty assessment in neural data.
• The combination of Laplace priors and posterior mean estimation is recommended for optimal GLM performance.