Machine Learning 01 - Basic Concept

最近开始学习Stanford吴恩达的机器学习课程，常做笔记，以便复习巩固。
鄙人才疏学浅，如有错漏与想法，还请多包涵，指点迷津。

Week 01

Introduction

• Application of machine learing
  
  • Database mining
  • Applications can’t program by hand
  • Customizing programs
• Definition
  
  • Arthur Samuen. Field of study that gives computers the ability to learn without being explicitly programmed.
  • Tom Mitchell. A computer program is said to learn from experience E with respect to some task T and some performance measure P, if its performance on T as measured by P improves with experience E.
• Common Types
  
  • Supervised Learning
    
    • Given the “right answer” for each example in the data.
    • Regreession Problem : Predict real-value output.
    • Classification : Predict discrete output.
  • Unsupercised learning
    
    • Unsupervised learning allows us to approach problems with little or no idea what the effect of the variables is.
    • Clustering、Non-clustering

Model and Cost Function

• Basic Model Representation
  
  • number of training data - m
  • Input - x
  • Output - y
  • Input space - X
  • Output space - Y
  • Hypothesis - h:X->Y
• Cost Function
  
  • Cost function measure the accuracy of our hypothesis function, for example :
    $$J(\theta _{0},\theta _{1})=\frac{1}{2m}\sum_{i=1}^{m}(\hat{y_{i}}-y_{i})^{2}=\frac{1}{2m}\sum_{i=1}^{m}(h_{\theta }(x_{i})-y_{i})^{2}$$
• Contour plot
  
  • A contour plot is a graph that contains many contour lines. A contour line of a two variable function has a constant value of the same line.

Parameter Learning

• Outline

  • Start with some $\theta _{0}, \theta _{1}$
  • Keep changing $\theta _{0}, \theta _{1}$ to reduce $J(\theta _{0}, \theta _{1})$ until we hopefully end up at a minimum.

• Algorithm

  repeat until convergence {
  

  $$\theta _{j}:=\theta _{j}-\alpha \frac{\partial }{\partial \theta _{0}}J(\theta _{0},\theta _{1}, ..., \theta_{n})\qquad\text{(for j = 0, 1, ..., n)}$$
  }
  simultaneous update {
  $\qquad$temp0:=$\theta _{0}-\alpha \frac{\partial }{\partial \theta _{0}}J(\theta _{0},\theta _{1}, ..., \theta_{n})$
  $\qquad$…
  $\qquad$tempn:=$\theta _{n}-\alpha \frac{\partial }{\partial \theta _{0}}J(\theta _{0},\theta _{1}, ..., \theta_{n})$
  $\qquad$$\theta _{0}$:=temp0
  $\qquad$…
  $\qquad$$\theta _{n}$:=tempn
  }

  • Comprehension
    
    • It’s like going down the hill in the fastest way. The differential give us a direction to move towards, and the $\alpha$(which is called learning rate) means the size of each step.
    • As we approach the bottom of our convex function, the derivative will tend to be 0, and at the bottom we have $\theta _{1}:=\theta _{1}-\alpha \times 0$.

• Gradient descent for linear regression - Algorthm1

  repeat until convergence (simultaneously update){
  $\qquad$$\theta _{0}:=\theta _{0}-\alpha\frac{1}{m}\sum_{m}^{i=1}(h_{\theta }(x^{(i)})-y^{i})$
  $\qquad$$\theta _{1}:=\theta _{1}-\alpha\frac{1}{m}\sum_{m}^{i=1}(h_{\theta }(x^{(i)})-y^{i})$
  }

  • This method looks at every example in the entire training set on every step, and is called batch gradient descent.