论文标题
贝叶斯回归的多级吉布斯抽样
Multilevel Gibbs Sampling for Bayesian Regression
论文作者
论文摘要
基于贝叶斯推理技术，贝叶斯回归仍然是一种简单但有效的工具。对于具有复杂后验分布的大规模应用，采用了马尔可夫链蒙特卡洛方法。为了改善马尔可夫链蒙特卡洛（Monte Carlo）方法的众所周知的计算负担，用于贝叶斯回归，我们开发了一种用于线性混合模型贝叶斯回归的多级Gibbs采样器。数据矩阵的级别层次结构是通过聚集数据矩阵的功能和/或样本来创建的。此外，研究了相关样品的使用以减少方差，以改善马尔可夫链的收敛性。对各种数据集进行测试，几乎所有这些数据集都可以加快预测性能损失。
Bayesian regression remains a simple but effective tool based on Bayesian inference techniques. For large-scale applications, with complicated posterior distributions, Markov Chain Monte Carlo methods are applied. To improve the well-known computational burden of Markov Chain Monte Carlo approach for Bayesian regression, we developed a multilevel Gibbs sampler for Bayesian regression of linear mixed models. The level hierarchy of data matrices is created by clustering the features and/or samples of data matrices. Additionally, the use of correlated samples is investigated for variance reduction to improve the convergence of the Markov Chain. Testing on a diverse set of data sets, speed-up is achieved for almost all of them without significant loss in predictive performance.
