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Abstract
Extracting relevant features from data sets where the number of observations n is much smaller then the number of predictors p is a major challenge in modern statistics. Sorted LOne Penalized Estimation (SLOPE)—a generalization of the lassois a promising method within this setting. Current numerical procedures for SLOPE, however, lack the efficiency that respective tools for the lasso enjoy, particularly in the context of estimating a complete regularization path. A key component in the efficiency of the lasso is predictor screening rules: rules that allow predictors to be discarded before estimating the model. This is the first paper to establish such a rule for SLOPE. We develop a screening rule for SLOPE by examining its subdifferential and show that this rule is a generalization of the strong rule for the lasso. Our rule is heuristic, which means that it may discard predictors erroneously. In our paper, however, we show that such situations are rare and easily safeguarded against by a simple check of the optimality conditions. Our numerical experiments show that the rule performs well in practice, leading to improvements by orders of magnitude for data in the p >> n domain, as well as incurring no additional computational overhead when n > p.
Original language  English 

Pages (fromto)  112 
Number of pages  12 
Journal  Advances in Neural Information Processing Systems 
Publication status  Published  2020 Dec 
Event  Neural Information Processing Systems  Duration: 0001 Jan 2 → … 
Subject classification (UKÄ)
 Probability Theory and Statistics
 Computational Mathematics
Free keywords
 screening rules
 lasso
 regression
 regularization
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Optimization and Algorithms for Sparse Regression
Larsson, J., Wallin, J. & Bogdan, M.
2018/12/03 → 2024/05/20
Project: Dissertation