正交设计矩阵加速贝叶斯半参数回归
Orthogonalized Design Matrices Speed-ups of Bayesian Semiparametric Regression
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中文总结 AI 辅助
研究如何用正交设计矩阵加速贝叶斯半参数回归，通过预循环重新表述模型，在列维度上使计算量大幅减少，实现约5到60倍加速。
中文摘要 AI 辅助
我们阐述了如何通过使用正交设计矩阵显著加速贝叶斯半参数回归拟合和推理过程。半参数回归中的设计矩阵包含预测观测值和数据基函数，贝叶斯半参数回归通常需要循环型方法。我们表明，涉及正交设计矩阵的贝叶斯半参数回归模型的预循环重新表述在列维度上能使计算量减少两个数量级。计算机实验显示这种简单范式能带来约5到60倍的加速。
英文摘要
We explain how important classes of Bayesian semiparametric regression fitting and inference procedures can be sped up, significantly, via the use of orthogonalized design matrices. Typically, design matrices in semiparametric regression contain predictor observations and basis functions of such data. In Bayesian semiparametric regression, loop-type approaches such as Gibbs sampling and coordinate ascent variational inference typically are required. We show that pre-loop reformulation of Bayesian semiparametric regression models involving orthogonalized design matrices lead to two orders of magnitude, with respect to column dimension, computational reduction. Our computer experiments reveal that this simple paradigm results in approximately 5- to 60-fold speed-ups.
