Machine Learning—Mixtures of Gaussians and the EM algorithm

网易公开课,第12,13课 notes,7a, 7b,8 从这章开始,介绍无监督的算法 对于无监督,当然首先想到k means, 最典型也最简单,有需要直接看7a的讲义   Mixtures of Gaussians 如果要理解Mixtures of Gaussians,那先回去复习一下Gaussians Discriminant Analysis,高斯判别分析 首先高斯判别分析是生成算法, 所以不会直接拟合p(y|x), 而是拟合p(x|y)p(y), 即p(x,y) p(y)符合伯努力分布,

混合高斯模型(Mixtures of Gaussians)和EM算法 主要内容: 1. 概率论预备知识 2. 单高斯模型 3. 混合高斯模型 4. EM算法 5. K-means聚类算法 一.概率论预备知识 1. 数学期望/均值.方差/标准差 设离散型随机变量X的分布律为 则称为X的数学期望或均值 设连续型随机变量X的概率密度函数(pdf)为 则其数学期望定义为: 随机变量X的方差: 随机变量X的标准差: 2. 正态分布.协方差 正态分布: 概率密度函数: 设(X,Y)为二维随机变量,若存在,则

混合高斯模型(Mixtures of Gaussians)和EM算法 这篇讨论使用期望最大化算法(Expectation-Maximization)来进行密度估计(density estimation). 与k-means一样,给定的训练样本是,我们将隐含类别标签用表示.与k-means的硬指定不同,我们首先认为是满足一定的概率分布的,这里我们认为满足多项式分布,,其中,有k个值{1,…,k}可以选取.而且我们认为在给定后,满足多值高斯分布,即.由此可以得到联合分布. 整个模型简单描述为对于每个

Acknowledgement to Stanford CS229. 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 i

1    Unsupervised Learning 1.1    k-means clustering algorithm 1.1.1    算法思想 1.1.2    k-means的不足之处 1.1.3    如何选择K值 1.1.4    Spark MLlib 实现 k-means 算法 1.2    Mixture of Gaussians and the EM algorithm 1.3    The EM Algorithm 1.4    Principal Components

Machine Learning Algorithms Study Notes 高雪松 @雪松Cedro Microsoft MVP 目 录 1    Introduction    1 1.1    What is Machine Learning    1 1.2    学习心得和笔记的框架    1 2    Supervised Learning    3 2.1    Perceptron Learning Algorithm (PLA)    3 2.1.1    PLA -- "知

A Gentle Guide to Machine Learning Machine Learning is a subfield within Artificial Intelligence that builds algorithms that allow computers to learn to perform tasks from data instead of being explicitly programmed. Got it? We can make machines lear

看到Max Welling教授主页上有不少学习notes,收藏一下吧,其最近出版了一本书呢还,还没看过. http://www.ics.uci.edu/~welling/classnotes/classnotes.html Statistical Estimation [ps]- bayesian estimation- maximum a posteriori (MAP) estimation- maximum likelihood (ML) estimation- Bias/Variance

from: http://www.metacademy.org/roadmaps/rgrosse/bayesian_machine_learning Created by: Roger Grosse(http://www.cs.toronto.edu/~rgrosse/) Intended for: beginning machine learning researchers, practitioners Bayesian statistics is a branch of statistics