Estimating Precision Matrices for High-Dimensional Interval-Valued Data

2026-05-14

AI Summary

This study addresses the challenge of accurately estimating precision matrices to characterize conditional dependence structures among variables in high-dimensional interval-valued data, where conventional methods often fail. The work proposes the first dedicated framework for this setting, assuming that the upper and lower bounds of intervals share a common graphical structure. It introduces an interval graphical lasso optimization model and develops an efficient convex optimization algorithm for its solution. The proposed method enjoys strong theoretical guarantees, including consistency and sparsity of the estimator, thereby substantially enhancing interpretability. Empirical evaluations on both synthetic and real-world datasets demonstrate its superior performance over existing approaches, particularly in precision matrix estimation and recovery of underlying graph structures.

Abstract

In the field of statistical learning and data analysis, estimating precision matrices (i.e., the inverse of covariance matrices) is a critical task, particularly for understanding dependency structures among variables. However, traditional methods often fall short when dealing with high-dimensional interval-valued data, where each observation is represented as an interval rather than a single point. This paper proposes a novel framework for estimating precision matrices in such contexts, addressing the unique challenges posed by the interval nature of the data. Specifically, we assume that the upper and lower bounds of the intervals share the same conditional dependency structure, and then formulate the interval graphical lasso optimization objective to estimate the precision matrix. At the optimization level, we provide an efficient computational approach, while at the theoretical level, we prove the sparsity and consistency of the estimator. Experimental results on simulated studies and real data applications demonstrate the superiority of the proposed method in terms of estimation precision and interpretability.

Problem

• precision matrix
• high-dimensional data
• interval-valued data
• conditional dependency
• statistical learning

Innovation

• precision matrix
• interval-valued data
• graphical lasso
• high-dimensional statistics
• conditional dependency