Graph-based Learning under Perturbations via Total Least-Squares.

Area of Science:

• Graph-based machine learning
• Network science
• Statistical modeling

Background:

• Graphs are essential for modeling complex data relationships in various fields.
• Key graph learning tasks include topology identification and signal inference.
• Structural Equation Models (SEMs) are used for topology identification but require extensive data.
• Existing signal inference methods often assume perfect topology, which is unrealistic.

Purpose of the Study:

• To develop a robust method for graph topology identification and signal inference that accounts for perturbations.
• To address limitations of conventional SEMs and signal inference approaches in real-world scenarios.
• To introduce a unified framework for handling signal or topology perturbations in graph learning.

Main Methods:

• A regularized total least-squares (TLS) approach is proposed.
• Iterative algorithms with convergence guarantees are developed to solve the TLS problem.
• Generalizations using structured and/or weighted TLS are explored for incorporating prior information on perturbations.

Main Results:

• The proposed TLS-based approach demonstrates effectiveness in both topology identification and signal inference tasks.
• The method shows robustness against perturbations like model mismatch, outliers, and adversarial behavior.
• Analyses using both simulated and real-world data validate the performance of the novel TLS approaches.

Conclusions:

• The novel regularized TLS approach provides a powerful and flexible tool for graph learning under perturbations.
• This work offers a unified solution for challenges in topology identification and signal inference.
• The findings have broad implications for various applications relying on graph analysis and machine learning.