Fast Exact Bayesian Inference for Sparse Signals in the Normal Sequence Model.
Fast Exact Bayesian Inference for Sparse Signals in the Normal Sequence Model.
复制标题
正态序列模型中稀疏信号的快速精确贝叶斯推理。
DOI：
10.1214/20-ba1227
复制
发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Botond Szabó
中科院分区：
文献类型：
--
作者：
T. Erven;Botond Szabó
我们考虑在稀疏正态序列模型中使用模型选择先验（包括尖峰和平板先验）进行贝叶斯推理的精确算法。由于现有的最佳精确算法对于超过 n=500 的样本量在数值上变得不稳定，因此人们对近似算法（吉布斯采样、变分贝叶斯等）、收缩先验（例如马蹄先验和 Spike-and-Slab LASSO）或经验贝叶斯方法等替代方法给予了很多关注。然而，通过引入在线顺序预测的算法思想，我们表明精确计算对于更大的样本量是可行的：对于一般模型选择先验，我们达到 n=25000，对于某些尖峰和平板先验，我们可以轻松达到 n=100000。我们进一步证明了有限样本量的类似 de Finetti 的结果，该结果准确地描述了哪些模型选择先验可以表示为尖峰和平板先验。最后，所提出方法的计算速度和数值准确性在模拟数据和前列腺癌数据集的实验中得到了证明。在我们的实验评估中，我们计算了所有新算法的数值精度的保证界限，这表明所提出的方法在数值上是可靠的，而基于长除法的替代方法则不然。
We consider exact algorithms for Bayesian inference with model selection priors (including spike-and-slab priors) in the sparse normal sequence model. Because the best existing exact algorithm becomes numerically unstable for sample sizes over n=500, there has been much attention for alternative approaches like approximate algorithms (Gibbs sampling, variational Bayes, etc.), shrinkage priors (e.g. the Horseshoe prior and the Spike-and-Slab LASSO) or empirical Bayesian methods. However, by introducing algorithmic ideas from online sequential prediction, we show that exact calculations are feasible for much larger sample sizes: for general model selection priors we reach n=25000, and for certain spike-and-slab priors we can easily reach n=100000. We further prove a de Finetti-like result for finite sample sizes that characterizes exactly which model selection priors can be expressed as spike-and-slab priors. Finally, the computational speed and numerical accuracy of the proposed methods are demonstrated in experiments on simulated data and on a prostate cancer data set. In our experimental evaluation we compute guaranteed bounds on the numerical accuracy of all new algorithms, which shows that the proposed methods are numerically reliable whereas an alternative based on long division is not.
影响因子：
7
作者：
Thomas, JG;Olson, JM;Zhao, LP
通讯作者：
Zhao, LP
贝叶斯块对角变量选择和模型平均。
影响因子：
2.7
作者：
Papaspiliopoulos,O;Rossell,D
通讯作者：
Rossell,D
影响因子：
1.4
作者：
E. George;R. McCulloch
通讯作者：
E. George;R. McCulloch