Enhancing Signal Proportion Estimation Through Leveraging Arbitrary Covariance Structures

2025-07-16

AI Summary

This paper addresses the problem of estimating the proportion of true signals among high-dimensional variables, overcoming restrictive assumptions—such as variable independence and signal sparsity—imposed by conventional methods. We propose a dependence-aware estimation framework based on Principal Factor Approximation (PFA), the first to incorporate PFA into signal proportion estimation. Our approach explicitly models arbitrary covariance structures and integrates lower-bound confidence estimation for dependence correction. Theoretically, we characterize the intrinsic interplay among signal sparsity, signal strength, and covariance dependence, and derive asymptotic consistency conditions both before and after dependence adjustment. Extensive simulations demonstrate that our method consistently outperforms state-of-the-art approaches across diverse covariance structures and sparsity levels, particularly enhancing weak-signal detection power and estimation accuracy.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation
• Machine Learning: Matrix & Tensor Methods

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Accurately estimating the proportion of true signals among a large number of variables is crucial for enhancing the precision and reliability of scientific research. Traditional signal proportion estimators often assume independence among variables and specific signal sparsity conditions, limiting their applicability in real-world scenarios where such assumptions may not hold. This paper introduces a novel signal proportion estimator that leverages arbitrary covariance dependence information among variables, thereby improving performance across a wide range of sparsity levels and dependence structures. Building on previous work that provides lower confidence bounds for signal proportions, we extend this approach by incorporating the principal factor approximation procedure to account for variable dependence. Our theoretical insights offer a deeper understanding of how signal sparsity, signal intensity, and covariance dependence interact. By comparing the conditions for estimation consistency before and after dependence adjustment, we highlight the advantages of integrating dependence information across different contexts. This theoretical foundation not only validates the effectiveness of the new estimator but also guides its practical application, ensuring reliable use in diverse scenarios. Through extensive simulations, we demonstrate that our method outperforms state-of-the-art estimators in both estimation accuracy and the detection of weaker signals that might otherwise go undetected.

Problem

• Estimating true signal proportion among many variables
• Overcoming limitations of independence assumptions in estimators
• Improving accuracy across varying sparsity and dependence structures

Innovation

• Leverages arbitrary covariance dependence information
• Incorporates principal factor approximation procedure
• Outperforms state-of-the-art estimators in accuracy