标题： 基于自适应收缩的高维线性回归的贝叶斯迁移学习 显示英文标题

标题： Bayesian Transfer Learning for High-Dimensional Linear Regression via Adaptive Shrinkage

摘要： 我们引入了BLAST，一种用于转移的贝叶斯线性回归自适应收缩方法，这是一个用于高维线性回归的贝叶斯多源迁移学习框架。所提出的分析框架结合全局-局部收缩先验和贝叶斯源选择，以平衡信息共享和正则化。我们展示了贝叶斯源选择如何提取最有用的数据源，同时减少可能导致负面迁移的偏倚信息。在该框架中，通过贝叶斯模型平均，源选择和稀疏回归在预测和推断中被联合考虑。我们的模型结构通过吉布斯采样算法允许高效的后验模拟，从而对目标回归系数进行完整的后验推断，使BLAST在计算上实用且推断简单。与仅基于目标数据的正则化方法相比，我们的方法在目标上的后验推断更准确，同时在预测性能上具有竞争力，并且在不确定性量化方面优于当前最先进的迁移学习方法。我们通过广泛的模拟研究验证了其有效性，并通过一个案例研究说明了其分析特性，该案例研究利用来自癌症基因组图谱（TCGA）的数据，从基因表达估计肿瘤突变负荷。 显示英文摘要

摘要： We introduce BLAST, Bayesian Linear regression with Adaptive Shrinkage for Transfer, a Bayesian multi-source transfer learning framework for high-dimensional linear regression. The proposed analytical framework leverages global-local shrinkage priors together with Bayesian source selection to balance information sharing and regularization. We show how Bayesian source selection allows for the extraction of the most useful data sources, while discounting biasing information that may lead to negative transfer. In this framework, both source selection and sparse regression are jointly accounted for in prediction and inference via Bayesian model averaging. The structure of our model admits efficient posterior simulation via a Gibbs sampling algorithm allowing full posterior inference for the target regression coefficients, making BLAST both computationally practical and inferentially straightforward. Our method achieves more accurate posterior inference for the target than regularization approaches based on target data alone, while offering competitive predictive performance and superior uncertainty quantification compared to current state-of-the-art transfer learning methods. We validate its effectiveness through extensive simulation studies and illustrate its analytical properties when applied to a case study on the estimation of tumor mutational burden from gene expression, using data from The Cancer Genome Atlas (TCGA).