Linear regression with constraint on the hypothesis set
When applying the onestep 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 onestep 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). 
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+1M columns (the column of ones may also be gone). The result will be a vector of d+1M weights.

All times are GMT 7. The time now is 04:07 PM. 
Powered by vBulletin® Version 3.8.3
Copyright ©2000  2020, Jelsoft Enterprises Ltd.
The contents of this forum are to be used ONLY by readers of the Learning From Data book by Yaser S. AbuMostafa, Malik MagdonIsmail, and HsuanTien Lin, and participants in the Learning From Data MOOC by Yaser S. AbuMostafa. No part of these contents is to be communicated or made accessible to ANY other person or entity.