 LFD Book Forum Linear regression with constraint on the hypothesis set
 User Name Remember Me? Password
 FAQ Calendar Mark Forums Read

 Thread Tools Display Modes
#1
 barbacot Junior Member Join Date: Apr 2013 Posts: 3 Linear regression with constraint on the hypothesis set

When applying the one-step equation for linear regression, the vector of weights is obtained directly with all its components.

What if we impose from the beginning a restriction on the form of the hypothesis, say h(x)=3+w1*x1, instead of the full linear form h(x)=w0+w1*x1? In other words, we want w0 to be 3, no matter what.

Is the one-step equation still applicable somehow?

To compare, if we were to apply the gradient descent with the same constraint, we could do it very easy, just by keeping w0 fixed at its initial value (3).
#2 yaser Caltech Join Date: Aug 2009 Location: Pasadena, California, USA Posts: 1,475 Re: Linear regression with constraint on the hypothesis set

Quote:
 Originally Posted by barbacot When applying the one-step equation for linear regression, the vector of weights is obtained directly with all its components. What if we impose from the beginning a restriction on the form of the hypothesis, say h(x)=3+w1*x1, instead of the full linear form h(x)=w0+w1*x1? In other words, we want w0 to be 3, no matter what. Is the one-step equation still applicable somehow? To compare, if we were to apply the gradient descent with the same constraint, we could do it very easy, just by keeping w0 fixed at its initial value (3).
You can transfer the fixed part to the other side of the equation, then solve for the remaining parameters only. In your example, it would be solving for only (the matrix would be a column vector of 's).
__________________
Where everyone thinks alike, no one thinks very much
#3
 barbacot Junior Member Join Date: Apr 2013 Posts: 3 Re: Linear regression with constraint on the hypothesis set

Thank you, sir, I think I finally got it. So if I want to pin down a number of M weights, I just move the constant M terms to the y vector (subtracting from it), and I am left with a matrix X with d+1-M columns (the column of ones may also be gone). The result will be a vector of d+1-M weights.

 Tags regression constraint Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off Forum Rules
 Forum Jump User Control Panel Private Messages Subscriptions Who's Online Search Forums Forums Home General     General Discussion of Machine Learning     Free Additional Material         Dynamic e-Chapters         Dynamic e-Appendices Course Discussions     Online LFD course         General comments on the course         Homework 1         Homework 2         Homework 3         Homework 4         Homework 5         Homework 6         Homework 7         Homework 8         The Final         Create New Homework Problems Book Feedback - Learning From Data     General comments on the book     Chapter 1 - The Learning Problem     Chapter 2 - Training versus Testing     Chapter 3 - The Linear Model     Chapter 4 - Overfitting     Chapter 5 - Three Learning Principles     e-Chapter 6 - Similarity Based Methods     e-Chapter 7 - Neural Networks     e-Chapter 8 - Support Vector Machines     e-Chapter 9 - Learning Aides     Appendix and Notation     e-Appendices

All times are GMT -7. The time now is 08:35 PM.

 Contact Us - LFD Book - Top

Powered by vBulletin® Version 3.8.3
Copyright ©2000 - 2019, Jelsoft Enterprises Ltd. The contents of this forum are to be used ONLY by readers of the Learning From Data book by Yaser S. Abu-Mostafa, Malik Magdon-Ismail, and Hsuan-Tien Lin, and participants in the Learning From Data MOOC by Yaser S. Abu-Mostafa. No part of these contents is to be communicated or made accessible to ANY other person or entity.