Computationally Sufficient Reductions for Joint Multiple Matrix Estimators with Sparsity and Fusion

TMLR Paper6935 Authors

Abstract:

We study a broad class of methods for the joint estimation of multiple sparse
symmetric matrices that incorporates group and fusion penalties for borrowing
strength across related matrices. This class includes extensions of popular
methods for precision and covariance matrix estimation as well as PCA. We show
that these methods can be unified through the lens of computational
sufficiency, a recently proposed theory that can reveal hidden commonalities
between seemingly disparate methods yielding both theoretical insights into
the underlying optimization problems and practical advantages in terms of
computational efficiency. We derive a universal screening rule that applies
simultaneously to all methods in this class, allowing us to reduce the search
space to block diagonal matrices. This enables streamlined algorithms that
drastically reduce the runtime, making the methods far more scalable and
practical for high-dimensional data analysis.

Submission Type: Regular submission (no more than 12 pages of main content)

Assigned Action Editor: ~Dan_Garber1

Submission Number: 6935