Variational log-Gaussian point-process methods for grid cells.

Area of Science:

• Computational Neuroscience
• Machine Learning
• Spatial Statistics

Background:

• Gaussian processes (GPs) offer data-efficient inference for neural tuning across time and space.
• Calculating spatial statistics for grid cells in large environments using GPs presents computational challenges.
• Log-Gaussian Poisson models are valuable for analyzing neural count data but can be computationally intensive.

Purpose of the Study:

• To present practical and computationally efficient methods for applying Gaussian-process (GP) techniques to spatial statistics.
• To enable the analysis of neural tuning in large-scale environments using GP models.
• To accelerate the estimation of log-Gaussian Poisson models within a variational Bayesian framework.

Main Methods:

• Development of specialized kernels for grid cell analysis within Gaussian-process models.
• Application of a variational Bayesian approach to log-Gaussian Poisson models for efficient computation.
• Implementation utilizing a low-rank spatial frequency subspace for accelerated calculations.

Main Results:

• Demonstrated rapid calculation of variational Bayesian log-Gaussian Poisson models.
• Achieved efficient estimation for specific posterior covariance parameterizations.
• Successfully applied the developed GP methods to experimental neural data.

Conclusions:

• The proposed Gaussian-process methods provide practical and accelerated solutions for spatial statistics in large environments.
• Variational Bayesian inference combined with low-rank approximations significantly enhances computational efficiency.
• These methods facilitate robust neural tuning inference from experimental data.