Transfer Learning under High-dimensional Generalized Linear Models.

Area of Science:

• Statistics
• Machine Learning
• Data Science

Background:

• Generalized Linear Models (GLMs) are widely used for statistical modeling.
• High-dimensional data presents unique challenges for statistical inference.
• Transfer learning offers a promising approach to enhance model performance by utilizing auxiliary data.

Purpose of the Study:

• To develop and analyze transfer learning algorithms for high-dimensional GLMs.
• To improve estimation and prediction error bounds by borrowing information from source data.
• To introduce an algorithm-free method for detecting informative source data.

Main Methods:

• Proposed a transfer learning algorithm for GLMs with theoretical analysis of estimation and prediction error bounds.
• Derived ℓ1/ℓ2-estimation error bounds and prediction error bounds.
• Introduced an algorithm-free source detection approach and proved its detection consistency.
• Developed an algorithm for constructing confidence intervals for coefficient components.

Main Results:

• Theoretical bounds show improved performance when source and target data are similar.
• The algorithm-free detection method is consistent under high-dimensional GLM transfer learning.
• Simulations and real-data experiments validated the effectiveness of the proposed algorithms.

Conclusions:

• The developed transfer learning approach enhances GLM performance in high-dimensional settings.
• The algorithm-free source detection is effective for identifying relevant auxiliary data.
• The R package `glmtrans` provides practical implementation for these methods.