The EM Algorithm/JerryLead 1、Introduction 在西瓜书中, EM算法是贝叶斯分类的扩展内容,用以解决训练样本含有“未观测变量”即隐变量(latent variable)的情形。然而,EM算法绝不仅仅于此,其在机器学习中占有十分重要的地位,k-means算法的核心思想就是EM算法的应用。本文主要介绍EM算法的原理,并给出EM算法的简单示例。
EM算法的全称为expectation-maximization algorithm,中文为最大期望算法,通常用来解决存在隐变量无法直接求解分布参数的问题。通过算法的名字我们就能猜出该算法和期望的计算相关,下面我们通过一个具体的例子来介绍和引入EM算法。 已知有100个男生和100个女生的身高数据,他们的身高数据满足于高斯分布,参数分别为男生N男生(...
expectation-maximization algorithmmultivariate datamissing valuesleast squaresHealy-Westmacott procedureSummary This chapter contains sections titled: Introduction Multivariate Data with Missing Values Least Squares with Missing Data Example 2.4: Multinomial with Complex Cell Structure Example 2.5: Analysis of PET...
If we suspect that the likelihood may have multiple local minima, we should use themultiple starts approach. In other words, we should run the EM algorithm several times with different starting values . Example: estimation of Gaussian mixtures The EM algorithm is often used to estimate the param...
EM算法 最大期望算法（Expectation-maximization algorithm，又译期望最大化算法）在统计中被 用于寻找，依赖于不可观察的隐性变量的概率 模型中，参数的最大似然估计。在统计计算中，最大期望算法是在概率模型中 寻找参数最大似然估计或者最大后验估计的算 法，其中概率模型依赖于无法观测的隐藏变量。最大期望...
Keywords:degradationdata;randomeffect;EMalgorithm CLCnumber:0213.2DocumentCOde-”A 退化数据分析的EM算法 徐安察,汤银才 f华东师范大学金融与统计学院,上海200241) 摘要:提出了用EM算法对产品可靠性进行分析.在退化模型中,当随机效应服从指数族分布 时,推导了参数估计的一般公式并且通过模拟评价了随机效应分布选取的敏感...
最大期望算法(Expectation Maximization Algorithm,又译期望最大化算法),是一种迭代算法,用于含有隐变量(hidden variable)的概率参数模型的最大似然估计或极大后验概率估计。 在统计计算中,最大期望(EM)算法是在概率(probabilistic)模型中寻找参数最大似然估计或者最大后验估计的算法,其中概率模型依赖于无法观测的隐藏变...
"Applications of the EM algorithm to the analysis of life-length data." Applied Statistics, 44, 323-341.J. R. G. Albert and L. A. Baxter, "Applications of the EM algorithm to the analysis of life length data," Applied Statistics, vol. 44, pp. 323-341, 1995....
Generative modeling is itself a kind of unsupervised learning task[1]. Given unlabelled data, To estimate the parameters, we can write the likelihood as which is also The EM algorithm can solve this pdf estimation iteratively. An example is provided here. The data points are drawn from 2 gaus...
Running the example fits the Gaussian mixture model on the prepared dataset using the EM algorithm. Once fit, the model is used to predict the latent variable values for the examples in the training dataset. Note: Your results may vary given the stochastic nature of the algorithm or evaluation...