Model averaging and dimension selection for the singular value decomposition
Model averaging and dimension selection for the singular value decomposition
复制标题
DOI：
10.1198/016214506000001310
复制
发表时间：
2007-06-01
影响因子：
3.7
通讯作者：
Hoff, Peter D.
中科院分区：
文献类型：
--
作者：
Hoff, Peter D.
许多用于m × n矩阵Y的多变量数据分析技术与模型Y = M + E相关，其中Y是满秩的m × 17矩阵，M是秩K <（m布尔与n）的未观察平均矩阵。通常，M的秩以启发式方式估计，然后通过Y的奇异值分解获得M的最小二乘估计，从而产生可能具有非常高方差的估计。在这篇文章中，我们提出了一种基于模型的替代方法，通过提供先验分布和后验估计的秩M和其奇异值分解的组件。除了提供更准确的推断之外，这种方法还具有可扩展到更一般的数据分析情况的优点，例如在存在缺失数据的情况下的推断和广义线性建模框架中的估计。
Many multivariate data-analysis techniques for an m x n matrix Y are related to the model Y = M + E, where Y is an m x 17 matrix of full rank and M is an unobserved mean matrix of rank K < (m boolean AND n). Typically the rank of M is estimated in a heuristic way and then the least-squares estimate of M is obtained via the singular value decomposition of Y, yielding an estimate that can have a very high variance. In this article we suggest a model-based alternative to the preceding approach by providing prior distributions and posterior estimation for the rank of M and the components of its singular value decomposition. In addition to providing more accurate inference, such an approach has the advantage of being extendable to more general data-analysis situations, such as inference in the presence of missing data and estimation in a generalized linear modeling framework.