Linear Regression with Multiple Variables
3 important questions on Linear Regression with Multiple Variables
Gradient Descent in practice II:
Should be decreasing after each iteration
- Automatic convergence test: For example, declare convergence if decreases by less than
in one iteration
- Visualize the cost function to verify that gradient descent is evolving
- For learning rate
, try increasing by 3x than previous attempt, if convergence is slow. Ex: ....0.001, .003,0.01, 0.3,1..
How to adjust features to match graph of the data: Polynomial Regression
If data doesn't look linear, and if thru visualization, it looks like it fits a different graph
Comparison: Gradient Descent vs. Normal Equations
Assume m training examples, n features
Rule of thumb: Good to move to gradient descent if n > 10,000
- Gradient Descent:
- Need to choose
- Need many iterations
- Works well even when n is large, complexity
- Need to choose
- Normal Equation:
- No need to choose Alpha learning rate
- Don't need to iterate
- Need to compute the Inverse
- Slow if n is very large, inversion has the complexity of
Rule of thumb: Good to move to gradient descent if n > 10,000
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