L(\theta|Y_{obs},Z)\propto\theta_1^{z_1+z_2}\theta_2^{z_3+z_4}\theta_3^{y_5} EM迭代公式: \hat{\theta}_1=\frac{z_1+z_2}{\sum_{i=1}^4z_i+y_5},\hat{\theta}_2=\frac{z_3+z_4}{\sum_{i=1}^4z_i+y_5},\hat{\theta}_3=\frac{y_5}{\sum_{i=1}^4...
EM中还有“硬”指定和“软”指定的概念,“软”指定看似更为合理,但计算量要大,“硬”指定在某些场合如K-means中更为实用(要是保持一个样本点到其他所有中心的概率,就会很麻烦)。 另外,EM的收敛性证明方法确实很牛,能够利用log的凹函数性质,还能够想到利用创造下界,拉平函数下界,优化下界的方法来逐步逼近极大值...
对应到 EM 上,E 步估计隐含变量,M 步估计其他参数,交替将极值推向最大。EM 中还有“硬”指定和“软”指定的概念,“软”指定看似更为合理,但计算量要大,“硬”指定在某些场合如K-means中更为实用(要是保持一个样本点到其他所有中心的概率,就会很麻烦)。 另外,EM 的收敛性证明方法确实很牛,能够利用 log ...
PRML 7: The EM Algorithm 1. K-means Clustering: clustering can be regarded as special parametric estimating problems with latent variables, which performs a hard assignment of data points to clusters in contrast to Gaussian Mixture Model introduced later....
In this chapter we study maximum likelihood estimation by the EM algorithm a special case of the MM algorithm. At the heart of every EM algorithm is some notion of missing data. Data can be missing in the ordinary sense of a failure to record certain observations on certain cases. Data ...
(EM算法)The EM Algorithm EM是我一直想深入学习的算法之一,第一次听说是在NLP课中的HMM那一节,为了解决HMM的参数估计问题,使用了EM算法。在之后的MT中的词对齐中也用到了。在Mitchell的书中也提到EM可以用于贝叶斯网络中。 下面主要介绍EM的整个推导过程。
The EM algorithm Since we are able to write the Gaussian mixture model as a latent-variable model, we can use theEM algorithmto find the maximum likelihood estimators of its parameters. Starting from an initial guess of the parameter vector ...
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This book presents an organized and well-knit account of the theory, methodology, extensions, and major applications of the Expectation-Maximization (EM) algorithm. It includes applications in the standard statistical contexts such as regression, factor analysis, variance components estimation, repeated-...
The EM Algorithm and Extensions remains the only single source to offer a complete and unified treatment of the theory, methodology, and applications of the EM algorithm. The highly applied area of statistics here outlined involves applications in regression, medical imaging, finite mixture analysis,...