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04-30-2013, 01:35 PM
 yaser Caltech Join Date: Aug 2009 Location: Pasadena, California, USA Posts: 1,477
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).
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