preface

Welcome to my blog.

For many reasons ,i decided to write [machine learning]’s learning notes blog with English,just simple English.

With the updating of my blog,i will also update this preface,especially for notations explain.

The notes are just for my study of machine learning course provided by Stanford University taught by Andrew.you can find the course videos at

http://open.163.com/special/opencourse/machinelearning.html,

also,you can download lecture notes and homework at

http://cimg3.163.com/edu/open/ocw/jiqixuexikecheng.zip

As for ML,in my view,is a application technology of statistics and probability theory ,which using linear algebra for computation,and as a kind of math tool to help us solve kinds of problems,such as big data,medical statistic,automatic driving and etc.

The notations using in this course are:

m : the number of training examples

x: input variable

y: output variable

n: the number of x(features)

(x,y): a single training example

(xix^i,yiy^i):the i th training example

n maybe be confused notation.

here is an example:

If we have a dataset of house price

area	price
2104	400
1600	330
2400	369

In the linear regression,we made the hypothesis function:

hθ(x)=θ0x0+θ1x1h_\theta(x) = \theta_0x_0+ \theta_1x_1

where x0=1x_0=1, x1x_1 means the area of the house.

Hence,m=3,

(x1x^1,y1y^1)=(2104,400),and n=1,because we only have one feature that is the area of the house.As for x and y,for instance,if we fit the parameters of the hypothesis function according these 3 training example,so that we can predict the price by given area,so,the given area is x,and the predicted price is y.

But in realistic,the effect factor may be more than the area,for example ,may contain the number of the bedrooms or others,now we have the datasat :

area	Number of bedroom	price
2104	3	400
1600	3	330
2400	3	369

Also,we update the our hypothesis function:

hθ(x)=θ0x0+θ1x1+θ2x2h_\theta(x) = \theta_0x_0+ \theta_1x_1+ \theta_2x_2

where x0=1x_0=1, x2x_2 means the area of the house, x1x_1

means the number of the bedrooms,

Hence,m=3

(x1x^1,y1y^1)=([x11x^1_1x12x^1_2],y1y^1)=([2104 3],400),where x is a vector,

n=2,because we have two features,area and number of the bedrooms.

BTW,mathjax is very strange but intreresting.neither way,i like mathtpye.