An elegant and powerful method for finding maximum likelihood solutions for models with latent variables is called the expectation-maximization algorithm. —— From 《Pattern Recognition and Machine Learning》 § 9.2.2 例子:三硬币模型,3枚硬币分别记为A、B、C,单独抛下正面出现的概率分别是ππ,p,q...
机器学习基础:期望最大化算法(Machine Learning Fundamentals: EM Algorithm) 前言EM算法和MLE算法的相同点在于,两者都需要知道确定的概率密度函数形式。 若没有隐藏变量,则可以用MLE进行估计。若数据欠缺,或存在隐含变量,则无法使用直接使用MLE进行估计,因此需要使用EM算法。 所谓的隐藏变量,指的是1. 在整个数据集中...
Nature Biotech在他的一篇EM tutorial文章《Do, C. B., & Batzoglou, S. (2008). What is the expectation maximization algorithm?. Nature biotechnology, 26(8), 897.》中,用了一个投硬币的例子来讲EM算法的思想。 比如两枚硬币A和B,如果知道每次抛的是A还是B,那可以直接估计(见下图a)。
E-Step. Estimate the missing variables in the dataset. M-Step. Maximize the parameters of the model in the presence of the data. The EM algorithm can be applied quite widely, although is perhaps most well known in machine learning for use in unsupervised learning problems, such as density ...
EM算法是一种迭代算法,由E步(求期望)和M步(求极值)两步组成,因此EM算法全称为期望极大算法(Expectation Maximum algorithm)。由于其是基础算法,因此在其他机器学习方法中常会用到,比如HMMEM算法的应用场合:如果我们要估计概率模型的参数,已知观测数据,那么一般会用极大似然估计法或者贝叶斯估计法,这在之前的逻辑斯蒂...
In this article, we propose two machine learning embedded algorithms for a class of semiparametric mixture models, where the mixing proportions and mean functions are unknown but smooth functions of covariates. Embedding machine learning techniques into a modified EM algorithm, the hybrid estimation ...
This algorithm is often considered for the solution of complex statistical problems with hidden data and we will show that it is also well suited for some NNs learning problems.This is a preview of subscription content, log in via an institution to check access. ...
(最早的文献是 1977 年 Dempster、Laird 和 Rubin 的Maximum likelihood from incomplete data via the EM algorithm),尽管切入点时常不同,但是感觉国内的学生(研究 machine learning)大部分还是停留在比较肤浅的角度,即便声称读过PRML也好EOSL也好,乃至任意一个讲述 machine learning 与 latent variable 相关的书籍、...
所以这一算法称为期望极大算法(expectation maximization algorithm),简称他们算望法。本章首先叙述EM算法,然后讨论EM算法的收敛性;作为EM算法的应用,介绍高斯混合模型的学习,最后叙述EM算法的推广——GEM算法。 9.1 EM算法的引入 概率模型有时既含有观测变量(observable variable),又含有隐变量或潜在变量(latent ...
介绍机器学习算法(Machine Learning Algorithms),如EM算法等、最小二乘法、感知机算法、支持向量机算法等。 一、 EM algorithm 简介 EM算法属于贝叶斯学派估计模型参数的方法。贝叶斯学派认为模型存在不可观测的隐变量Z控制着可观测量X,隐变量Z服从不可观测的Q分布,而可观测量分布P(X)是其联合分布P(X,Z)的边缘分布...