论文标题
在高斯模型空间中的模型选择不变由对称性
Model selection in the space of Gaussian models invariant by symmetry
论文作者
论文摘要
我们考虑了随机变量的多元中心高斯模型$ z =（z_1，\ ldots，z_p）$，在$ \ {1，\ ldots，p \} $的一组排列子组的作用下不变。使用对称组的代表理论，我们得出了协方差参数$σ$的最大似然估计的分布，以及diaConis-ylvisaker conjugate的标准化常数的分析表达，用于精度参数$ k =σ^{ - 1} $。因此，我们可以通过对称组的子组的作用进行完整的高斯模型中的贝叶斯模型选择，我们也可以称之为完整的RCOP模型。我们用一个尺寸$ 4 $的玩具示例和几个在环状组中进行选择的玩具示例来说明结果，其中包括一个高维示例，其中$ p = 100 $。
We consider multivariate centered Gaussian models for the random variable $Z=(Z_1,\ldots, Z_p)$, invariant under the action of a subgroup of the group of permutations on $\{1,\ldots, p\}$. Using the representation theory of the symmetric group on the field of reals, we derive the distribution of the maximum likelihood estimate of the covariance parameter $Σ$ and also the analytic expression of the normalizing constant of the Diaconis-Ylvisaker conjugate prior for the precision parameter $K=Σ^{-1}$. We can thus perform Bayesian model selection in the class of complete Gaussian models invariant by the action of a subgroup of the symmetric group, which we could also call complete RCOP models. We illustrate our results with a toy example of dimension $4$ and several examples for selection within cyclic groups, including a high dimensional example with $p=100$.
