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Title: An attention algorithm for solving large scale structured $l_{0}$-norm penalized estimation problems Authors:  Tso-Jung Yen - Academia Sinica (Taiwan) [presenting]
Yu-Min Yen - National Chengchi University (Taiwan)
Abstract: Technology advances have enabled researchers to collect large amounts of data with lots of covariates. Because of the high volume (large $n$) and high variety (large $p$) properties, model estimation with such kind of big data has posed great challenges for statisticians. We focus on the algorithmic aspect of these challenges. We propose a numerical procedure for solving large scale regression estimation problems involving a structured $l_{0}$-norm penalty function. This numerical procedure blends the ideas of randomization, proximal operators and blockwise coordinate descent algorithms. In particular, it adopts an attention-based sampling distribution for picking up regression coefficients for updates based on a closed form representation of the proximal operator of the structured $l_{0}$-norm penalty function. Simulation study shows the proposed numerical procedure is competitive to the benchmark algorithm for sparse estimation in terms of runtime and statistical accuracy when both the sample size and the number of covariates become large.