# A unified precision matrix estimation framework via sparse column-wise inverse operator under weak sparsity

arXiv: https://arxiv.org/abs/2107.02999 · HTML: https://mlsanity.com/paper/2107.02999/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jul 2021.

## Built on by (most cited first, 1 of 1)

- [Distributed Semi-Supervised Sparse Statistical Inference](https://mlsanity.com/paper/2306.10395/) (2023)

## Abstract (arXiv)

In this paper, we estimate the high dimensional precision matrix under the weak sparsity condition where many entries are nearly zero. We revisit the sparse column-wise inverse operator (SCIO) estimator citeliu2015fast and derive its general error bounds under the weak sparsity condition. A unified framework is established to deal with various cases including the heavy-tailed data, the non-paranormal data, and the matrix variate data. These new methods can achieve the same convergence rates as the existing methods and can be implemented efficiently.