An Improved Modified Cholesky Decomposition Method for Precision Matrix Estimation
This incremental improvement addresses a specific issue in statistical estimation for applications like classification, but is not broadly transformative.
The paper tackles the problem of variable order uncertainty in modified Cholesky decomposition for sparse precision matrix estimation by combining estimates from multiple permutations and using thresholding, achieving competitive performance in simulations and real-data classification.
The modified Cholesky decomposition is commonly used for precision matrix estimation given a specified order of random variables. However, the order of variables is often not available or cannot be pre-determined. In this work, we propose to address the variable order issue in the modified Cholesky decomposition for sparse precision matrix estimation. The key idea is to effectively combine a set of estimates obtained from multiple permutations of variable orders, and to efficiently encourage the sparse structure for the resultant estimate by the thresholding technique on the ensemble Cholesky factor matrix. The consistent property of the proposed estimate is established under some weak regularity conditions. Simulation studies are conducted to evaluate the performance of the proposed method in comparison with several existing approaches. The proposed method is also applied into linear discriminant analysis of real data for classification.