Multiple features

Multiple features

Notation:

• n = number of features
• = input (features) of training example.
• = value of feature j in training example.

For convenience of notation, define

向量內(nèi)積
Multivariate linear regression

Gradient descent for multiple variables

Hypothesis:
Parameters: （a n+1 dimensional vector）
Cost function:

Gradient descent:
Repeat {

}

Feature Scaling

Idea:Make sure features are on a similar scale

一般認(rèn)為在就可以認(rèn)為是可以的
Feature Scaling:Get every feature into approximately a range.
Mean normalization:Replace with to make features have approximately zero mean.(Do not apply to )

Learning rate

1. Make sure gradient descent is working correctly.
   should decrease on every iteration.But if is too small, gradient descent can be slow to converge.

Features and Polynomial Regression

Normal Equation

Normal equation: Method to solve for ananlytically.

Octave:pinv(x'*x)*x'*y

m training examples, n features

Gradient Descent

• Need to choose
• Needs many iterations
• Works well even when n is large

Normal Equation

• No need to choose
• Don't need to iterate
• Need to compute
• Slow if is very large(less than 10000)

Normal Equation Nonivertibility (Optional)

What if is non-invertible?

• Redundant features (linearly dependent)
• Too many features(e.g. )
  這種情況極少出現(xiàn)