More Powerful Selective Inference for the Graph Fused Lasso.

Area of Science:

• Statistics
• Machine Learning
• Data Science

Background:

• The graph fused lasso is effective for reconstructing piecewise constant signals on graphs.
• Existing methods for testing differences in means of graph-fused-lasso-estimated components lack control over selective Type I error.
• A naive z-test does not adequately address the data-dependent nature of the hypothesis.

Purpose of the Study:

• To develop a new statistical test for detecting differences in means between two connected components estimated via graph fused lasso.
• To ensure the proposed test controls the selective Type I error.
• To enhance statistical power compared to existing approaches.

Main Methods:

• Development of a novel hypothesis testing procedure tailored for graph fused lasso outputs.
• The method is designed to control the selective Type I error.
• The approach conditions on less information, aiming for improved statistical power.

Main Results:

• The proposed test effectively controls the selective Type I error.
• The new method demonstrates substantially higher statistical power than existing procedures.
• The approach was validated through simulations and real-world datasets.

Conclusions:

• The developed test provides a statistically sound and more powerful way to compare means of graph-fused-lasso-estimated components.
• The method offers improved discovery rates on datasets related to public health, such as drug overdose and birth rates.
• This work advances signal reconstruction and hypothesis testing in graph-based data analysis.