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#1
08-07-2012, 04:57 AM
 itooam Senior Member Join Date: Jul 2012 Posts: 100
Q4) h(x) = ax

This question is similar to that in the lectures i.e.,

in the lecture H1 equals

h(x) = ax + b

Is this question different to the lecture in the respect we shouldn't add "b" (i.e., X0 the bias/intercept) when applying? Or should I treat the same?

My confusion is because in many papers etc a bias/intercept is assumed even if not specified i.e., h(x) = ax could be considered the same as h(x) = ax + b
#2
08-07-2012, 05:24 AM
 yaser Caltech Join Date: Aug 2009 Location: Pasadena, California, USA Posts: 1,478
Re: Q4) h(x) = ax

Quote:
 Originally Posted by itooam This question is similar to that in the lectures i.e., in the lecture H1 equals h(x) = ax + b Is this question different to the lecture in the respect we shouldn't add "b" (i.e., X0 the bias/intercept) when applying? Or should I treat the same? My confusion is because in many papers etc a bias/intercept is assumed even if not specified i.e., h(x) = ax could be considered the same as h(x) = ax + b
There is no bias/intercept in this problem, only the slope (one parameter which is ).
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#3
08-07-2012, 05:36 AM
 itooam Senior Member Join Date: Jul 2012 Posts: 100
Re: Q4) h(x) = ax

Thanks for comfirmation, much appreciated
#4
01-31-2013, 11:16 AM
 geekoftheweek Member Join Date: Jun 2012 Posts: 26
Re: Q4) h(x) = ax

Is there a best way to minimize the mean-squared error? I am doing gradient descent with a very low learning rate (0.00001) and my solution is diverging! not converging. Is it not feasible to do gradient descent with two points when approximating a sine?
Thanks
#5
01-31-2013, 12:09 PM
 geekoftheweek Member Join Date: Jun 2012 Posts: 26
Re: Q4) h(x) = ax

Never mind, I got my solution to converge, though I do not trust my answer. Oh well.
#6
01-31-2013, 04:34 PM
 sanbt Member Join Date: Jan 2013 Posts: 35
Re: Q4) h(x) = ax

Quote:
 Originally Posted by geekoftheweek Never mind, I got my solution to converge, though I do not trust my answer. Oh well.
You can use linear regression to calculate each hypothesis.
(since linear regression is basically analytical formula for minimizing mean square error).

Also, you can confirm if your g_bar from simulation makes sense by calculate it directly. (calculate expectation of the hypothesis from each (x1,x2) over [-1,1] x [-1,1] ). This involves two integrals but you can plug in the expression to wolfram or mathematica.
#7
04-30-2013, 03:55 AM
 jlevy Junior Member Join Date: Apr 2013 Posts: 5
Re: Q4) h(x) = ax

Quote:
 Originally Posted by geekoftheweek Is there a best way to minimize the mean-squared error? Thanks
Just use w=inv(X`*X)*X`*Y
and note that X has just a single column (no column of 1's).
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#8
03-04-2016, 07:13 AM
 khohi Member Join Date: Dec 2015 Posts: 10
Re: Q4) h(x) = ax

Great

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