Machine Learning - Stanford - Coursera
1.0.0
1.0.0
  • Acknowledgements
  • Introduction
  • Linear Algebra Review
  • Types of Machine Learning
  • Supervised Learning
    • Linear Regression
      • Linear Regression in One Variable
        • Cost Function
        • Gradient Descent
      • Multivariate Linear Regression
        • Cost Function
        • Gradient Descent
        • Feature Scaling
        • Mean Normalization
        • Choosing the Learning Rate α
    • Polynomial Regression
      • Normal Equation
      • Gradient Descent vs. Normal Equation
Powered by GitBook
On this page

Was this helpful?

  1. Supervised Learning

Polynomial Regression

It is not necessary for us to always use only the features that we have. If needed, we can sometimes create new features using the existing ones that might be more suitable for the given problem.

For example, if we have length and width, we can use them to form a new feature named area and perform linear regression using this new feature.

Polynomial Regression is very similar to multivariate linear regression. Each xix_ixi​ could be a degree of a given feature.

For example,

hθ(x)=θ0+θ1x1+θ2x2+θ3x3h_\theta(x) = \theta_0 + \theta_1x_1 + \theta_2x_2 + \theta_3x_3hθ​(x)=θ0​+θ1​x1​+θ2​x2​+θ3​x3​

where x1=size, x2=(size)2, x3=(size)3x_1 = size, \, x_2=(size)^2, \, x_3=(size)^3x1​=size,x2​=(size)2,x3​=(size)3

However, while using Polynomial Regression, it is very important to scale the features for gradient descent to work properly.

We can decide to use Polynomial Regression in any manner, i.e. we can even write our hypothesis as:

hθ(x)=θ0+θ1(size)+θ2(size)1/2+θ3(size)1/3h_\theta(x) = \theta_0 + \theta_1(size) + \theta_2(size)^{1/2} + \theta_3(size)^{1/3}hθ​(x)=θ0​+θ1​(size)+θ2​(size)1/2+θ3​(size)1/3

Later, we discuss how certain algorithms help us in choosing what features to use and how to use them efficiently.

PreviousChoosing the Learning Rate αNextNormal Equation

Last updated 5 years ago

Was this helpful?