Multivariate Temporal Point Process Regression.

Area of Science:

• Computational Neuroscience
• Statistical Modeling
• Machine Learning

Background:

• Point process data are increasingly prevalent across scientific disciplines.
• Analyzing high-dimensional neuronal spike trains requires advanced statistical methods.

Purpose of the Study:

• To propose a novel point process regression model for high-dimensional response and predictor data.
• To address challenges in dimensionality reduction and interpretation of complex point process relationships.

Main Methods:

• Developed a point process regression model using basis transferring functions in a convolutional manner.
• Organized coefficients into a three-way tensor, imposing low-rank, sparsity, and subgroup structures.
• Designed a scalable optimization algorithm for parameter estimation and derived theoretical guarantees.

Main Results:

• The proposed model effectively reduces dimensionality and integrates information across individual processes.
• Demonstrated accurate parameter estimation and consistent subgroup identification, even with diverging dimensions.
• Validated through simulations and a real-world analysis of cross-area neuronal spike trains.

Conclusions:

• The novel point process regression model offers a powerful tool for analyzing high-dimensional point process data, particularly in neuroscience.
• The imposed tensor structures enhance interpretability and analytical efficiency.
• The method shows significant promise for future applications in complex data analysis.