Greedy Ridge Estimation for Large Precision Matrix

• Activity Number: 510
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Shiqiong Huang*+ and Jiashun Jin and Zhigang Yao
• Companies: Carnegie Mellon and Carnegie Mellon and Swiss Federal Institute of Technology
• Keywords: high dimension ; greedy algorithm ; partial correlation ; precision matrix ; ridge regression ; sparsity

Abstract

Estimating sparse precision matrix is an important problem for high dimensional data. We propose a row-by-row estimation approach in the core of which is a greedy screening algorithm. For each row, greedy screening identifies a subset S as candidates for the nonzero coordinates in this row of precision matrix. We show that under mild conditions, S contains the true support as a subset and it is sufficient for estimating this row. S also has a size that remains relatively small. Such properties of the greedy screening is then used to develop a fast algorithm to estimate the corresponding row of a precision matrix. In real data analysis, we introduce ridge regression to our greedy screening algorithm to solve the problem of singularity in correlation matrix. We apply Greedy Ridge Estimation to gene micro array data. The algorithm is fast, memory efficient and we get good classification results.