2021/12/03 by Cai, Jian-Feng, Cardoso, José Vinícius de M., Palomar, Daniel P. +1 · 1 citation
#FOS: Computer and information sciences #Machine Learning (cs.LG)
paper · doi:10.48550/arxiv.2112.01939
We study the problem of estimating precision matrices in Gaussian distributions that are multivariate totally positive of order two (MTP2). The precision matrix in such a distribution is an M-matrix. This problem can be formulated as a sign-constrained log-determinant program. Current algorithms are designed using the block coordinate descent method or the proximal point algorithm, which becomes computationally challenging in high-dimensional cases due to the requirement to solve numerous nonnegative quadratic programs or large-scale linear systems. To address this issue, we propose a novel algorithm based on the two-metric projection method, incorporating a carefully designed search direction and variable partitioning scheme. Our algorithm substantially reduces computational complexity, and its theoretical convergence is established. Experimental results on synthetic and real-world datasets demonstrate that our proposed algorithm provides a significant improvement in computational efficiency compared to the state-of-the-art methods.