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A significance test for graph-constrained estimation.

Sen Zhao1, Ali Shojaie1

  • 1Department of Biostatistics, University of Washington, Seattle, Washington, U.S.A.

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Summary
This summary is machine-generated.

This study introduces the Grace test for graph-constrained estimation, providing reliable uncertainty measures and p-values. It offers improved statistical power, even with imperfect graph information, enhancing variable selection accuracy.

Keywords:
Biological networksGraph-constrained estimationHigh-dimensional dataSignificance testVariable selection

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Area of Science:

  • Statistics
  • Machine Learning
  • High-Dimensional Data Analysis

Background:

  • Graph-constrained estimation methods leverage covariate relationships for improved accuracy, particularly in high-dimensional settings.
  • Existing methods lack uncertainty measures and are sensitive to inaccurate graph structures, potentially compromising estimate reliability.
  • Variable selection is crucial for identifying relevant covariates associated with a response.

Purpose of the Study:

  • To develop a novel inference framework, the Grace test, that incorporates external graph information for coefficient estimation and uncertainty quantification.
  • To ensure the proposed method controls Type-I error rates robustly, irrespective of the accuracy of the provided graph structure.
  • To enhance statistical power compared to existing methods, especially when the graph information is informative, and to address scenarios with partially informative graphs.

Main Methods:

  • Introduction of the Grace test, a new inference framework integrating external graph information into estimation and p-value generation.
  • Theoretical analysis and numerical simulations to evaluate the asymptotic properties of the Grace test, including Type-I error control and statistical power.
  • Development of a Grace-ridge test to improve power in settings where the external graph is not fully informative.

Main Results:

  • The Grace test asymptotically controls the Type-I error rate regardless of the graph's accuracy.
  • When the graph is informative, the Grace test demonstrates superior asymptotic power compared to methods ignoring external information.
  • The Grace-ridge test offers enhanced statistical power when the graph is only partially informative, outperforming existing approaches.

Conclusions:

  • The Grace test provides a reliable framework for inference in graph-constrained estimation, offering uncertainty measures and robust Type-I error control.
  • The proposed methods, Grace test and Grace-ridge test, significantly improve statistical power when external graph information is reasonably informative.
  • These advancements offer more reliable and powerful variable selection in high-dimensional settings by effectively utilizing graph structures.