Part of Advances in Neural Information Processing Systems 36 (NeurIPS 2023) Main Conference Track
Jian-Feng CAI, José Vinícius de Miranda Cardoso, Daniel Palomar, Jiaxi Ying
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.