A proximal distance algorithm for likelihood-based sparse covariance estimation.

Area of Science:

• Statistics
• Machine Learning
• Computational Biology

Background:

• Estimating covariance matrices with sparsity is crucial in high-dimensional data analysis.
• Existing methods often involve thresholding or shrinkage penalties, which can induce unwanted bias.
• Patternless sparsity requires specialized estimation techniques beyond standard approaches.

Purpose of the Study:

• To develop a novel likelihood-based method for covariance matrix estimation under patternless sparsity.
• To regularize the distance from the covariance estimate to a symmetric sparsity set, avoiding common norm penalty issues.
• To provide an efficient and robust algorithm for sparse covariance estimation.

Main Methods:

• A likelihood-based approach regularizing distance to a symmetric sparsity set.
• Optimization via solving a sequence of smooth, unconstrained subproblems.
• Proximal distance majorization-minimization principle for subproblem generation and solution.

Main Results:

• The proposed algorithm is rapid, handles more parameters than cases, and yields positive-definite solutions.
• It demonstrates superior performance across various metrics in simulated experiments compared to competing methods.
• Analysis of international migration and flow cytometry data shows improved dependency network inference.

Conclusions:

• The new method offers an effective alternative to thresholding and shrinkage for sparse covariance estimation.
• It provides more accurate marginal and conditional dependency networks, particularly for cell signaling data.
• The approach is computationally efficient and statistically robust, with desirable convergence properties.