Regularized parameter estimation in high-dimensional gaussian mixture models.
Regularized parameter estimation in high-dimensional gaussian mixture models.
复制标题
DOI：
10.1162/neco_a_00128
复制
发表时间：
2011-06
影响因子：
2.9
通讯作者：
Zou H
中科院分区：
文献类型：
--
作者：
Ruan L;Yuan M;Zou H
有限高斯混合模型由于其极大的灵活性，在统计学中得到了广泛的应用。然而，高维混合高斯模型的参数估计具有挑战性，因为需要估计的参数很多。在这封信中，我们提出了一种惩罚似然估计来解决这一困难。我们对逆协方差矩阵施加的ℓ-1型惩罚鼓励了其条目的稀疏性，从而有助于降低问题的有效维度。我们证明了所提出的估计可以使用期望最大化算法来有效地计算。为了说明该方法的实用价值，我们考虑了它在基于模型的聚类和混合判别分析中的应用。模拟数据和真实数据的数值实验表明，该方法是一种有价值的高维数据分析工具。
Finite gaussian mixture models are widely used in statistics thanks to their great flexibility. However, parameter estimation for gaussian mixture models with high dimensionality can be challenging because of the large number of parameters that need to be estimated. In this letter, we propose a penalized likelihood estimator to address this difficulty. The ℓ1-type penalty we impose on the inverse covariance matrices encourages sparsity on its entries and therefore helps to reduce the effective dimensionality of the problem. We show that the proposed estimate can be efficiently computed using an expectation-maximization algorithm. To illustrate the practical merits of the proposed method, we consider its applications in model-based clustering and mixture discriminant analysis. Numerical experiments with both simulated and real data show that the new method is a valuable tool for high-dimensional data analysis.