Fast maximum likelihood estimation using continuous-time neural point process models.

Area of Science:

• Computational Neuroscience
• Statistical Modeling
• Neuroscience

Background:

• Neural recording technology is rapidly advancing, increasing the number of simultaneously recorded neurons.
• Discrete-time point process models are commonly used for neural activity analysis but are computationally intensive.
• Maximum-likelihood estimation in discrete-time models requires significant time and memory, especially with fine time binning.

Purpose of the Study:

• To develop a more efficient statistical method for analyzing neural activity.
• To reduce the computational burden and memory requirements of neural data analysis.
• To provide a faster and more convenient alternative to existing discrete-time point process models.

Main Methods:

• Utilized continuous-time models of neural activity.
• Employed Gaussian quadrature for optimal efficiency.
• Analyzed memory requirements and computation times, comparing O(np) to O(qp) and O(np(2)) to O(qp(2)).
• Assessed accuracy using physiological considerations, error bounds, and mathematical results.

Main Results:

• Continuous-time models with Gaussian quadrature dramatically decrease memory and computation time when the number of parameters (p) is less than the number of time-bins (n).
• In 95% of hippocampal recordings, a quadrature order (q) of 60 resulted in negligible numerical error.
• The proposed method avoids discretization errors inherent in discrete-time models.

Conclusions:

• Statistical inference using continuous-time models is a fast and memory-efficient alternative to discrete-time models.
• The methodology retains the statistical power of discrete-time inference while improving performance.
• This approach is suitable for analyzing large-scale neural recordings.