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Old 04-30-2013, 01:35 PM
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yaser yaser is offline
Join Date: Aug 2009
Location: Pasadena, California, USA
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Default Re: Linear regression with constraint on the hypothesis set

Originally Posted by barbacot View Post
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 w_1x_1=y-3 solving for w_1 only (the matrix {\rm X} would be a column vector of x_1's).
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