Scaling the Poisson GLM to massive neural datasets through polynomial approximations

Area of Science:

• Computational Neuroscience
• Statistical Modeling
• Neurotechnology

Background:

• Large-scale neural recordings capture activity from thousands of neurons.
• Existing statistical methods struggle with the high dimensionality of this data.
• Efficient analysis is crucial for understanding complex brain functions.

Purpose of the Study:

• Develop scalable approximate inference methods for Poisson generalized linear models (GLMs).
• Adapt polynomial approximation techniques for efficient neural data analysis.
• Enable accurate statistical inference on high-dimensional neural datasets.

Main Methods:

• Utilized polynomial approximations for approximate sufficient statistics in Poisson GLMs.
• Employed quadratic approximations for nonlinear terms in the log-likelihood with Gaussian priors.
• Derived closed-form solutions for estimates and posterior distributions.
• Introduced an adaptive procedure for selecting polynomial approximation intervals.

Main Results:

• Developed a highly scalable method requiring only a single pass over the data.
• Achieved efficient and accurate inference and regularization of high-dimensional parameters.
• Successfully fitted a fully-coupled Poisson GLM to 831 mouse neurons over 41 minutes.
• Analyzed over 2 billion spike count bins, identifying fine-timescale neural dependencies.

Conclusions:

• The proposed methods offer efficient and accurate analysis of large-scale neural recordings.
• This approach advances statistical methods for neural data analysis.
• Enables deeper understanding of neural circuit dynamics and information processing.