Computation-Risk Tradeoffs for Covariance-Thresholded Regression

Dinah Shender, John Lafferty
Proceedings of the 30th International Conference on Machine Learning, PMLR 28(3):756-764, 2013.

Abstract

We present a family of linear regression estimators that provides a fine-grained tradeoff between statistical accuracy and computational 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 parameter. With appropriate parameter choices, the estimate is the solution to a sparse, diagonally dominant linear system, solvable in near-linear time. Our analysis shows how the risk varies with the sparsity and regularization level, thus establishing a statistical estimation setting for which there is an explicit, smooth tradeoff between risk and computation. Simulations are provided to support the theoretical analyses.

Cite this Paper

BibTeX
@InProceedings{pmlr-v28-shender13, title = {Computation-Risk Tradeoffs for Covariance-Thresholded Regression}, author = {Shender, Dinah and Lafferty, John}, booktitle = {Proceedings of the 30th International Conference on Machine Learning}, pages = {756--764}, year = {2013}, editor = {Dasgupta, Sanjoy and McAllester, David}, volume = {28}, number = {3}, series = {Proceedings of Machine Learning Research}, address = {Atlanta, Georgia, USA}, month = {17--19 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v28/shender13.pdf}, url = {https://proceedings.mlr.press/v28/shender13.html}, abstract = {We present a family of linear regression estimators that provides a fine-grained tradeoff between statistical accuracy and computational 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 parameter. With appropriate parameter choices, the estimate is the solution to a sparse, diagonally dominant linear system, solvable in near-linear time. Our analysis shows how the risk varies with the sparsity and regularization level, thus establishing a statistical estimation setting for which there is an explicit, smooth tradeoff between risk and computation. Simulations are provided to support the theoretical analyses.} }
Endnote
%0 Conference Paper %T Computation-Risk Tradeoffs for Covariance-Thresholded Regression %A Dinah Shender %A John Lafferty %B Proceedings of the 30th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2013 %E Sanjoy Dasgupta %E David McAllester %F pmlr-v28-shender13 %I PMLR %P 756--764 %U https://proceedings.mlr.press/v28/shender13.html %V 28 %N 3 %X We present a family of linear regression estimators that provides a fine-grained tradeoff between statistical accuracy and computational 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 parameter. With appropriate parameter choices, the estimate is the solution to a sparse, diagonally dominant linear system, solvable in near-linear time. Our analysis shows how the risk varies with the sparsity and regularization level, thus establishing a statistical estimation setting for which there is an explicit, smooth tradeoff between risk and computation. Simulations are provided to support the theoretical analyses.
RIS
TY - CPAPER TI - Computation-Risk Tradeoffs for Covariance-Thresholded Regression AU - Dinah Shender AU - John Lafferty BT - Proceedings of the 30th International Conference on Machine Learning DA - 2013/05/26 ED - Sanjoy Dasgupta ED - David McAllester ID - pmlr-v28-shender13 PB - PMLR DP - Proceedings of Machine Learning Research VL - 28 IS - 3 SP - 756 EP - 764 L1 - http://proceedings.mlr.press/v28/shender13.pdf UR - https://proceedings.mlr.press/v28/shender13.html AB - We present a family of linear regression estimators that provides a fine-grained tradeoff between statistical accuracy and computational 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 parameter. With appropriate parameter choices, the estimate is the solution to a sparse, diagonally dominant linear system, solvable in near-linear time. Our analysis shows how the risk varies with the sparsity and regularization level, thus establishing a statistical estimation setting for which there is an explicit, smooth tradeoff between risk and computation. Simulations are provided to support the theoretical analyses. ER -
APA
Shender, D. & Lafferty, J.. (2013). Computation-Risk Tradeoffs for Covariance-Thresholded Regression. Proceedings of the 30th International Conference on Machine Learning, in Proceedings of Machine Learning Research 28(3):756-764 Available from https://proceedings.mlr.press/v28/shender13.html.

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