论文标题
在半监督期望最大化上
On the Semi-supervised Expectation Maximization
论文作者
论文摘要
当数据不完整时，期望最大化（EM）算法被广泛用作迭代修改，以最大似然估计。我们专注于半监督案例，以从标记和未标记的样本中学习模型。半监督案例中的现有工作主要集中在绩效而不是融合保证上，但是我们专注于标记的样品对收敛率的贡献。该分析清楚地表明，标记的样品如何提高指数家族混合模型的收敛速率。在这种情况下，我们假设在全球融合的社区中，人口EM（具有无限数据的EM）是针对仅由未标记的样本组成的人口EM的。标记样品的分析提供了对高斯混合模型的收敛速率的全面描述。此外，我们扩展了标记样品的发现，并为人口EM的收敛率与未标记的样品提供了替代证明，用于对称混合物的两个高斯人。
The Expectation Maximization (EM) algorithm is widely used as an iterative modification to maximum likelihood estimation when the data is incomplete. We focus on a semi-supervised case to learn the model from labeled and unlabeled samples. Existing work in the semi-supervised case has focused mainly on performance rather than convergence guarantee, however we focus on the contribution of the labeled samples to the convergence rate. The analysis clearly demonstrates how the labeled samples improve the convergence rate for the exponential family mixture model. In this case, we assume that the population EM (EM with unlimited data) is initialized within the neighborhood of global convergence for the population EM that consists solely of samples that have not been labeled. The analysis for the labeled samples provides a comprehensive description of the convergence rate for the Gaussian mixture model. In addition, we extend the findings for labeled samples and offer an alternative proof for the population EM's convergence rate with unlabeled samples for the symmetric mixture of two Gaussians.
