A tuning-free and scalable method for joint graphical model estimation with sharper bounds

• DOI: 10.48550/arxiv.2503.18722
• Publication Date: 2025-03-24
• Authors: Shixiang Liu; Yanhang Zhang; Zhifan Li; Jia‐Xin Yin
• Keywords: Graphical model

Joint estimation of multiple graphical models (i.e., precision matrices) has emerged as an important topic in statistics. Unlike separate estimation, joint can leverage shared structural patterns across graphs to yield more accurate results. In this paper, we present efficient and tuning-free method named MIGHT (Multi-task Iterative Graphical Hard Thresholding) jointly estimate models. We reformulate the model into a series multi-task learning problems column-by-column manner, then solve these by using iterative algorithm based on hard thresholding operator. Theoretically, derive non-asymptotic error bound for our method. prove that, under proper signal conditions, attains selection consistency improved bound, also exhibits asymptotic normality -- properties rarely explored existing literature. The performance is validated through numerical simulations real data analysis cancer gene-expression RNA-seq dataset.