Learning High-dimensional Generalized Linear Autoregressive Models.

Area of Science:

• Statistics
• Machine Learning
• Network Science

Background:

• Vector autoregressive models are widely used for time series analysis and network structure inference.
• Existing methods lack statistical guarantees in non-Gaussian settings, limiting their application.

Purpose of the Study:

• To develop statistical guarantees for parameter and network structure estimation in non-Gaussian autoregressive models.
• To extend generalized linear models to include Poisson and Bernoulli autoregressive processes.

Main Methods:

• A sparsity-regularized maximum likelihood estimator is proposed.
• Martingale concentration inequalities and empirical process techniques for dependent data are employed.
• Sample complexity bounds are derived to analyze estimator performance.

Main Results:

• Novel theoretical bounds are established for the proposed estimator.
• The impact of network parameters on estimator performance is characterized.
• Simulation studies validate the derived bounds and estimator effectiveness.

Conclusions:

• The study provides a robust framework for statistical inference in non-Gaussian autoregressive networks.
• The findings advance the understanding of network structure estimation in complex time series data.
• The developed methods offer improved reliability for applications in social, biological, and financial networks.