1. Machine Learning and Linear Regression (with 1 variable)

Introduction to Machine Learning

1. Machine Learning Algorithms

• supervised learning
• unsupervised learning
• others: reinforcement learning, recommendation systems

2. Supervised Learning

• right answers (labels)
• Regression: predict continuous output (e.g., housing price)
• Classification: discrete valued output (e.g., tumor)
• support vector machine can manage infinite number of features.

3. Unsupervised Learning

• no labels
• clustering: automatically find structure of data w/o specific algorithms
• examples: google news clustering, gene analysis, market segmentation, astronomical data analysis, social network analysis, organize computing clusters
• cocktail party algorithm: two audio recording separates out two overlapped voices.
  Programing environment: Octave, matlab
  [W, s, v] = svd((repmat(sum(x.*x, 1), size(x, 1), 1). *x)*x')

Linear Regression

1. Model Representation

• how do we represent h?
• Given a training set, to learn a function h: x-> y so that h(x) is a good predictor for y value.
  

2. Cost Function

• cost function, squared error function
  
• goal is to minize the cost function J
  
• 3D (height = cost)
  
• contour plots(figures)
  same color line has the same cost
  

3. Gradient Descent

• start at a random point and move toward the lowest point through calculating the steepest descent.
  
• gradient descent algorithm
  
  calculate all parameters simultaneously for each iteration.
  
• alpha(learning rate)
• Regardless of slope's sign, theta1 converges to the minimum
  
• if alpha is too small or too big
  
• With a fixed alpha, derivative gets smaller as approaching the minimum as the slope gets smaller, thus, the steps get smaller.
  

Applying gradient descent to linear algebra

• Convergence for theta0 and 1 at the same time.
  
  

• The cost function for a linear algebra is always a convex function (bowl-shaped function). Thus, no local minimum. Always converges to a global minimum.

• batch gardient descent: each step uses all training examples.