＜监督和无监督学习＞Introduction to Machine Learning

Definition

• Machine learning is field of study thaht gives computers the ability to learn withuot being explicitly programmed.

Machine Learning Algorithms

• Supervised learning
• Unsupervised learning
• Recommender system
• Reinforcement learning

Supervised Learning

Basic Concept

• Input and its corresponding right answer give labels then test the module with brand new input

• Example:

  

• Types

  • Regression: a particular type of supervise learning, is predict a number from infinitely many possible outputs

    

  • Classification : predict catagories, finited possible outputs (classes/catogories may be many, so do the inputs)

  

Linear Regression Model

• Terminology
  • x = "input" variable = feature
  • y = "output" variable = "taget" variable
  • m = number of training examples
  • (x,y) = single training example
  • 
  • w,b = parameter = coefficients = weights
  • w is slope while b is y-intercept

• The process of unsupervise learning

  • Univariable linear regression = one variable linear regression

• Cost function ------ find w and b （额外除以2目的是方便后面梯度下降求导时把2约去使式子看起来更简洁）

  • Squared error cost function (To find different value when choosing w and b)

  • For linear regression with the squared error cost function, you always end up with a bow shape or a hammock shape.

    ==

  • The difference between fw(x) and J(w)

    • the previous one is related to x and we choose different w for J(w)

Gradient descent

• The method of find the minimal J(w,b)
• Every time ture 360 degree to have a little step and find the intermediate destination with the the largest difference with the last point, then do the same until you find you couldn't go down anymore
• process (so called "Batch" gradient descent)
  • start with some w,b (set w=b=0)
  • keep chaging w,b to reduce J(w,b)
  • Until we settle at or near a minimum
• If you find different minimal result by choosing different starting point, all these different results are calledlocal minima
• Gradient descent algorithm

  • 

    |--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
    | α = learning rate (usually a small positive number bwtween 0 to 1)：decide how large the step I take when going down to the hill (dJ(w,b)/dw) destinate in which direction you want to take your step |

  • 

  • The end condition: w and b don't change much with each addition step that you take

  • Tip: b and w must be updated simultaneously

  • WHY THEY MAKE SENSE?

  • Learning rate α

    |--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
    | Problem1: When α is too small, the gradient makes sense but is too slow Problem2: When α is too big, it may overshoot, never reach the minimal value of J(w) Problem3: When the starting point is the local minima, the result will stop at the local minima (Can reach locak minimum with fixed learning rate) 所以！α是要根据坡度变化而变化的！！ |

Learning Regression Algorithm

• For square error cost function, there only one minima

Unsupervise Learning

• Finding something interesting in unlabeled data：Data only comes with inputs x, but not outputs label y. Algrithm has to find structure in the data

• Types

  • Clustering : Group similar data points together

    

    

    

    

  • Anomaly detection :Find unusual data points

  • Dimensionality redution: Compress data using fewer numbers