LFD Book Forum questions 5 & 6
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#1
01-31-2013, 01:01 PM
 geekoftheweek Member Join Date: Jun 2012 Posts: 26
questions 5 & 6

Once we find an average hypothesis, we have to compute and . In order to compute the expectation values of bias/var wrt x, I assume we need to generate a *new* set of points. Correct? How big should that set be?
#2
01-31-2013, 02:45 PM
 geekoftheweek Member Join Date: Jun 2012 Posts: 26
Re: questions 5 & 6

...or are we just supposed to use the points generated in order to calculate g_bar? That would mean that bias and var have twice as many points to average over than the number of data sets used to calculate g_bar, because each data set had two two data points.
#3
01-31-2013, 04:23 PM
 sanbt Member Join Date: Jan 2013 Posts: 35
Re: questions 5 & 6

So to calculate g_bar you used 2 points to get each hypothesis and average over them.

Now Bias and var should come from the entire range of the real line. I would say
about hundreds range from -1 to 1.
#4
02-01-2013, 11:26 AM
 geekoftheweek Member Join Date: Jun 2012 Posts: 26
Re: questions 5 & 6

Quote:
 Originally Posted by sanbt Now Bias and var should come from the entire range of the real line. I would say about hundreds range from -1 to 1.
Are you saying generate 100 new points?
#5
02-01-2013, 05:57 PM
 sanbt Member Join Date: Jan 2013 Posts: 35
Re: questions 5 & 6

Quote:
 Originally Posted by geekoftheweek Are you saying generate 100 new points?
yes
#6
02-01-2013, 10:30 PM
 gah44 Invited Guest Join Date: Jul 2012 Location: Seattle, WA Posts: 153
Re: questions 5 & 6

All these are approximating integrals.

Many problems really are sums, but this one is, theoretically, continuous.

First you do 2D integrals to compute a, a 1D integral to compute bias,
and a 3D integral to compute variance.

(I think it would also work to compute bias+variance in the first place, and subtract bias to get variance, but I didn't try that.)

I used equally space points for all, but you could also use random points.

If I was in the right mood, I might have done Gaussian quadrature, or some other numerical integration method.

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