Q4) h(x) = ax

[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

[yaser]

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 ).

[itooam]

Thanks for comfirmation, much appreciated

[geekoftheweek]

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

[geekoftheweek]

Never mind, I got my solution to converge, though I do not trust my answer. Oh well.

[sanbt]

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.

[jlevy]

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).

[khohi]

Great

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