机器学习与神经网络

分享者：曹逸君

从贝叶斯说起

begin with bayes

$$P(A|B)=\frac { P(A\cap B) }{ P(B) } =\frac { P(B|A)\cdot P(A) }{ P(B) }$$

简单得令人尴尬

Embarrassedly Simple

基本上就是数数

Basically you just Counts

垃圾邮件过滤

Spam Filter

朴素贝叶斯

Naive Bayes

马尔科夫链

Markov Chain

自然语言生成

Natural Language Generator

贝叶斯的局限

Limits of Bayes

无法捕捉输入间关系

Unable capture relations between input

需要大量的数据

Quadratic increase with feature dimensions

神经网络

Neural Network

$$ \begin{pmatrix} x_0 & x_1 & x_2 & x_3 & \cdots & x_n \\ \end{pmatrix} \cdot \begin{pmatrix} w_{0,1} & w_{0,2} \\ w_{1,1} & w_{1,2} \\ w_{2,1} & w_{2,2} \\ w_{3,1} & w_{3,2} \\ \vdots & \vdots \\ w_{n,1} & w_{n,2} \\ \end{pmatrix} = \begin{pmatrix} z_1 & z_2 \\ \end{pmatrix} $$

$$ \begin{pmatrix} a_1 & a_2 \end{pmatrix} = \begin{pmatrix} sigmoid(z_1) & sigmoid(z_2) \end{pmatrix} $$

$$ sigmoid(t) = \frac{1}{1+e^{-t}} $$

异或函数

XOR

$$ \quad X \quad \quad Y \\ \begin{eqnarray} 0\quad 0 & = & 0 \\ 0\quad 1 & = & 1 \\ 1\quad 0 & = & 1 \\ 1\quad 1 & = & 0 \end{eqnarray} $$

代价函数

Cost Function

$$ J(\Theta )=\frac { 1 }{ m } \left[ \sum _{ i=1 }^{ m }{ \sum _{ k=1 }^{ K }{ { y }_{ k }^{ (i) }log({ h }_{ \Theta }({ x }^{ (i) }))_{ k }+(1-{ y }^{ (i) })(1-(h_{ \Theta }(x^{ (i) }))_{ k }) } } \right] \\ +\frac { \lambda }{ 2m } \sum _{ l=1 }^{ L-1 }{ \sum _{ i=1 }^{ s_{ l } }{ \sum _{ j=1 }^{ s_{ l }+1 }{ (\Theta _{ ij }^{ (l) })^{ 2 } } } } $$