Large-Scale Sparse Inverse Covariance Estimation via Thresholding and Max-Det Matrix Completion

Authors: Richard Zhang, Salar Fattahi, Somayeh Sojoudi

ICML 2018 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental The algorithm is highly efficient in practice: we solve the associated MDMC problems with as many as 200,000 variables to 7-9 digits of accuracy in less than an hour on a standard laptop computer running MATLAB. In Section 4, we present computation results on a suite of test cases. Both synthetic and real-life graphs are considered.
Researcher Affiliation Academia 1Department of Industrial Engineering and Operations Research, University of California, Berkeley, USA. 2Department of Electrical Engineering and Computer Science, University of California, Berkeley, USA.
Pseudocode Yes Figure 1. MATLAB code for chordal embedding via its internal approximate minimum degree ordering. Given a sparse matrix (C), compute a chordal embedding (Gt) and the number of added edges (m). p = amd(C); % fill-reducing ordering [h,~,~,~,R] = symbfact(C(p,p)); Gt = R+R'; Gt(p,p) = Gt; m = nnz(R)-nnz(tril(C));
Open Source Code Yes MATLAB source code: http://alum.mit.edu/www/ ryz.
Open Datasets Yes The actual graphs (i.e. the sparsity patterns) for Σ 1 are chosen from Suite Sparse Matrix Collection (Davis & Hu, 2011) a publicly available dataset for large-and-sparse matrices collected from real-world applications.
Dataset Splits No The paper describes how synthetic and real-life graphs are used, and how samples are generated, but it does not specify explicit training, validation, or test dataset splits (e.g., 80/10/10 percentages or specific sample counts for each split).
Hardware Specification Yes All experiments are performed on a laptop computer with an Intel Core i7 quad-core 2.50 GHz CPU and 16GB RAM.
Software Dependencies Yes The reported results are based on a serial implementation in MATLAB-R2017b.
Experiment Setup Yes Our implementation used γ = 0.01 and ρ = 0.5. Both our Newton decrement threshold and QUIC s convergence threshold are 10 7. In all of our simulations, the threshold λ is set so that the number of nonzero elements in the the estimator is roughly the same as the ground truth.