Bayesian Discriminant Analysis Using a High Dimensional Predictor
Bayesian Discriminant Analysis Using a High Dimensional Predictor
复制标题
使用高维预测器的贝叶斯判别分析
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
S. Ghosal
中科院分区：
文献类型：
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作者：
Xingqi Du;S. Ghosal
我们考虑的问题贝叶斯判别分析使用高维预测。在这种情况下，只有假设一些适当的额外结构（如稀疏性），才能以合理的精度估计潜在的精度矩阵。通过对精度矩阵的Cholesky分解的稀疏先验，推导出精度矩阵的先验.为了便于计算，我们使用收缩先验来诱导Cholesky分解矩阵的非对角项的稀疏性，并利用一定的条件共轭结构。我们得到的收缩率的后验分布的平均值和精度矩阵分别使用欧几里德和Frobenius距离，并表明，在一些温和的限制下的增长的维度，误分类概率的贝叶斯分类过程收敛到Oracle分类器的线性和二次判别分析。大量的模拟表明，所提出的贝叶斯方法性能非常好。应用程序，以识别癌性乳腺肿瘤的基础上获得的图像数据，使用查找针抽吸被认为是。
We consider the problem of Bayesian discriminant analysis using a high dimensional predictor. In this setting, the underlying precision matrices can be estimated with reasonable accuracy only if some appropriate additional structure like sparsity is assumed. We induce a prior on the precision matrix through a sparse prior on its Cholesky decomposition. For computational ease, we use shrinkage priors to induce sparsity on the off-diagonal entries of the Cholesky decomposition matrix and exploit certain conditional conjugacy structure. We obtain the contraction rate of the posterior distribution for the mean and the precision matrix respectively using the Euclidean and the Frobenius distance, and show that under some milder restriction on the growth of the dimension, the misclassification probability of the Bayesian classification procedure converges to that of the oracle classifier for both linear and quadratic discriminant analysis. Extensive simulations show that the proposed Bayesian methods perform very well. An application to identify cancerous breast tumorbased on image data obtained using find needle aspirate is considered.