Abstract
We present a family of linear regression es- timators that provides a fine-grained trade- off between statistical accuracy and computa- tional efficiency. The estimators are based on hard thresholding of the sample covariance matrix entries together with l2 -regularizion (ridge regression). We analyze the predictive risk of this family of estimators as a function of the threshold and regularization param- eter. With appropriate parameter choices, the estimate is the solution to a sparse, di- agonally dominant linear system, solvable in near-linear time. Our analysis shows how the risk varies with the sparsity and regulariza- tion level, thus establishing a statistical esti- mation setting for which there is an explicit, smooth tradeoff between risk and computa- tion. Simulations are provided to support the theoretical analyses.
Author
Diane Shender and John Lafferty
Journal
Proceedings of the 30th International Conference on Ma- chine Learning
Paper Publication Date
2013
Paper Type
Astroinformatics