naosk8 / machine-learning-knowledge

knowledge memo of machine-learning

machine-learning-knowledge

knowledge memos/citations of machine-learning based on a coursera class: Machine Learning by Andrew Ng.

What is machine learning? (Two definitions)

• Arthur Samuel's older and informal definition:
  "the field of study that gives computers the ability to learn without being explicitly programmed."

• Tom Mitchell's more modern definition:
  "A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P, if its performance at tasks in T, as measured by P, improves with experience E."

  • Example: playing checkers.
  • E = the experience of playing many games of checkers
  • T = the task of playing checkers.
  • P = the probability that the program will win the next game.

In general, any machine learning problem can be assigned to one of two broad classifications:
Supervised learning and Unsupervised learning.

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Supervised Learning and Unsupervised Learning

Supervised Learning

Definition

• "right answer" is given.
• In supervised learning, we are given a data set and already know what our correct output should look like, having the idea that there is a relationship between the input and the output.

Categories

• Regression (回帰)
  • we are trying to predict results within a continuous output, meaning that we are trying to map input variables to some continuous function.
  • ex. Given a picture of Male/Female, we have to predict his/her age on the basis of the given picture.
• Classification (分類)
  • we are instead trying to predict results in a discrete output. In other words, we are trying to map input variables into discrete categories
  • ex. Given a patient with a tumor, we have to predict whether the tumor is malignant or benign.

Unsupervised Learning

Definition

• Approaching problems with little or no idea what our results should look like.
• We can derive structure from data where we don't necessarily know the effect of the variables.
• We can derive this structure by clustering the data based on relationships among the variables in the data.
• With unsupervised learning there is no feedback based on the prediction results.

Categories

• Clustering
  • ex. Take a collection of 1,000,000 different genes, and find a way to automatically group these genes into groups that are somehow similar or related by different variables, such as lifespan, location, roles, and so on.
• Non-clustering
  • ex. The "Cocktail Party Algorithm", allows you to find structure in a chaotic environment. (i.e. identifying individual voices and music from a mesh of sounds at a cocktail party).

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Cost Function

Definition

• summation of the difference between the predicted value and the actual value.
• goal of machine learning to solove problem is, in other words, to minimize a cost function.
• it is also called "Squared error function" or "Mean squared error".

Equasion

• 1/m with Summation: averaging it
• 1/2 : we rather play with smaller numbers than big numbers
• If all data(x) are plotted on the hypothesis, cost function = 0.

Visual Image

• ex. h(X) = θ0 + θ1 * X

3D plot	Contour plot/figure

Two ways to minimize cost function

• Gradient Descent (any case)
• Normal Equation (n = # of features < 10,000)
  

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Gradient Descent

Definition

• Start with some θ(parameter)
• Keep changing θ to reduce J(θ) until we end up at a minimum
• "Batch" Gradient Descent: Each step of gradient descent uses all the training examples.

Algorithm

• As we approach a local minimum, gradient descent will automatically take smaller steps.
  So, no need to decrease α over time.

Caution

correct	incorrect

• Gradient descent could be stuck at local optima.

Technics about efficiency

• make each of input values in roughly the same range to converge efficiently, speedy.
• ideal range: −1 ≤ x(i) ≤ 1 or −0.5 ≤ x(i) ≤ 0.5
• Feature Scailing + Mean Normalization:

Feature Scaling

• "S" in the formula written above.
• divide the input values by the range (i.e. max - min) of the input variable.

Mean Normalization

• "μ" in the formula written above.
• subtract the average value from the values for that input variable.
• the average of the processed values is 0.

Learning Rate

• "α" in the gradient descent formula.
• If α is too small: slow convergence.
• If α is too large: may not decrease on every iteration and thus may not converge.

Normal Equation

Definition

• minimize J by explicitly taking its derivatives with respect to the θj ’s, and setting them to zero.
• This allows us to find the optimum theta without iteration.
  

Notice

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Linear Regression

name	logic
Model
Cost Function
Algorithm

Linear Regression for Multiple variables

• Every formula is equal.

description	formula
Expanded
X:column(vector)
X:row

Gradient Descent behind it

• simultaneously update
  　

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Binary Classification Problem(0 or 1)

• Logistic Function / Sigmoid Function

Hypothesis

• 0 <= h(x) <= 1
  
  
  
  

Key Concept

Decision Boundary

• In order to get our discrete 0 or 1 classification, we can translate the output of the hypothesis function as follows:
  

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Appendix

Expression in equation

Label	Definition
x	input variable, feature
y	output/target variable
m	number of training examples
h	logic(relation) between x and y
θ	parameter in h
J	cost function
α	learning rate
	real number

• Wiki: Table of expressions in math