Transfer Learning for High-Dimensional Linear Regression: Prediction, Estimation and Minimax Optimality.

Transfer Learning for High-Dimensional Linear Regression: Prediction, Estimation and Minimax Optimality.
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DOI:
10.1111/rssb.12479
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发表时间:
2022-03
期刊:
Journal of the Royal Statistical Society. Series B, Statistical methodology
影响因子:
--
通讯作者:
Li H
Li H
中科院分区:
其他
文献类型:
--
作者:
Li S;Cai TT;Li H

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本文考虑了在迁移学习环境中高维线性回归的估计和预测,其中除了来自目标模型的观测值之外,还可以使用来自不同但可能相关的回归模型的辅助样本。当信息辅助研究的集合是已知的,估计和预测,并建立其最优性。预测和估计的最优收敛速度比不使用辅助样本的相应速度快。这意味着可以转移来自信息丰富的辅助样本的知识,以提高目标问题的学习性能。当信息辅助样本集未知时,我们提出了一种数据驱动的迁移学习过程,称为Trans-Lasso,并展示了其对非信息辅助样本的鲁棒性及其在知识迁移中的效率。所提出的程序被证明在数值研究中,并适用于一个数据集的基因表达之间的关联。结果表明,trans-Lasso通过将来自多个不同组织的数据作为辅助样本,提高了靶组织中基因表达预测的性能。
This paper considers estimation and prediction of a high-dimensional linear regression in the setting of transfer learning where, in addition to observations from the target model, auxiliary samples from different but possibly related regression models are available. When the set of informative auxiliary studies is known, an estimator and a predictor are proposed and their optimality is established. The optimal rates of convergence for prediction and estimation are faster than the corresponding rates without using the auxiliary samples. This implies that knowledge from the informative auxiliary samples can be transferred to improve the learning performance of the target problem. When the set of informative auxiliary samples is unknown, we propose a data-driven procedure for transfer learning, called Trans-Lasso, and show its robustness to non-informative auxiliary samples and its efficiency in knowledge transfer. The proposed procedures are demonstrated in numerical studies and are applied to a dataset concerning the associations among gene expressions. It is shown that Trans-Lasso leads to improved performance in gene expression prediction in a target tissue by incorporating data from multiple different tissues as auxiliary samples.
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发表时间: 2019-03-01
期刊: NATURE GENETICS
影响因子: 30.8
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