Machine Learning A Probabilistic Perspective 笔记

最新推荐文章于 2020-08-04 17:33:51 发布

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最新推荐文章于 2020-08-04 17:33:51 发布

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文章标签：机器学习笔记

本文链接：https://blog.youkuaiyun.com/phoenix198425/article/details/78640513

这篇笔记主要探讨了《Machine Learning A Probabilistic Perspective》一书中关于随机变量和常见概率分布的内容，包括离散分布和连续分布的理论，如二项式系数和误差函数在机器学习中的应用。

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                    Random Values: 
 
   Concept 
   Meaning 
  
   Discrete Random Variables 
    
   Probability mass function / pmf 
   P() 
  
   判别分类器 Discriminative Classifier 
   P(Y=c|x) 
  
   生成分类器 Generative Classifier 
   P(Y=c|x)=P(Y=c|θ)P(x|Y=c,θ)∑c′P(Y=c′|θ)P(x|Y=c′,θ) 
  
   Unconditionally / marginally independent 
   P(x,y)=P(x)P(y) 
  
   Conditionally independent 
   P(x,y|z)=P(x|z)P(y|z) 
  
   P(x,y|z)=g(x,z)h(y,z),∀x,y,z such that P(z)>0 
  
   Continuous Random Variables 
    
   Cumulative distribution function / cdf 
   F(x)=P(X≤x) 
  
   Probability density function / pdf 
   f(x)=dF(x)dx 
  
   α Quantile of F 
   F−1(α)=xα such that P(X≤xα)=α 
  
   Median

Concept	Meaning
Discrete Random Variables
Probability mass function / pmf	$P()$
判别分类器 Discriminative Classifier	$P(Y=c \| x)$
生成分类器 Generative Classifier	$P(Y=c\|x) = \frac {P(Y=c\|\theta) P(x\|Y=c, \theta)} {\sum _{c'}P(Y=c'\|\theta) P(x\|Y=c', \theta)}$
Unconditionally / marginally independent	$P(x, y) =P(x) P(y)$
Conditionally independent	$P(x, y\|z) = P(x\|z)P(y\|z)$
	$P(x, y\|z) = g(x, z) h(y, z), \forall x, y,z$ such that $P(z) >0$
Continuous Random Variables
Cumulative distribution function / cdf	$F(x) = P(X \le x)$
Probability density function / pdf	$f(x) = \frac { \operatorname{d} F(x) } { \operatorname{d} x }$
$\alpha$ Quantile of F	$F^{-1}(\alpha) = x_{\alpha}$ such that $P(X \le x_\alpha) = \alpha$
Median