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-   -   *ANSWER* Questions 4-6 of Hwk 4 (bias and variance) (http://book.caltech.edu/bookforum/showthread.php?t=430)

 gmathew 05-02-2012 12:21 PM

*ANSWER* Questions 4-6 of Hwk 4 (bias and variance)

I solved this problem very carefully many times. But I am not getting the answers given in the homework solution for 5 and 6. These are the answers I am getting.

I am getting ghat = 1.4272x
bias = 0.5413
variance = 0.4725

Is anybody else getting similar answers? Can the intructor please verify the answers given in the homework solution?

thanks

 Iverson 05-04-2012 05:34 AM

Re: Questions 4-6 of Hwk 4 (bias and variance)

I got :
y = 1.4305x
bias : 0.2804
variance : 0.2381

My results for the bias and the variance are quite different from yours. I'm not sure they are correct though.

 danielfm 05-04-2012 12:37 PM

Re: Questions 4-6 of Hwk 4 (bias and variance)

I got:

gbar = 1.415863
bias = 0.261949
variance = 0.231310

Of course the results of each run vary, but if I round the numbers to 1 decimal place I always get bias = 0.3 and variance = 0.2.

 cassio 05-05-2012 07:00 PM

Re: Questions 4-6 of Hwk 4 (bias and variance)

Quote:
 Originally Posted by gmathew (Post 1797) I solved this problem very carefully many times. But I am not getting the answers given in the homework solution for 5 and 6. These are the answers I am getting. I am getting ghat = 1.4272x bias = 0.5413 variance = 0.4725 Is anybody else getting similar answers? Can the intructor please verify the answers given in the homework solution? thanks
there is a good discussion about these problems :D

 ramin 08-02-2012 06:05 AM

Re: Questions 4-6 of Hwk 4 (bias and variance)

Maybe don't forget that the expectation "integral" has a p(x) term in it, and p(x) is uniform in the interval [-1,1]

 dtyrp 05-03-2017 09:54 PM

Re: *ANSWER* Questions 4-6 of Hwk 4 (bias and variance)

Bump for interest in question 6! And I can't access the above link that cassio posted a few years ago:)

I'm able to get gbar and calculate the bias correctly but calculating the variance still has me stumped.

Here's my thought process:

To calculate variance, compute the integral of (g(x) - gbar(x))^2*p(x) from x = -1 to x = 1. Do this for each hypothesis g in your your hypothesis set (I generated 1000 different g's). p(x) is the uniform distribution that produces your x-axis data points. Now the expected value of a uniform random variable from -1 to 1 is 1/(1- -1) or 1/2. So the integral you calculate for each hypothesis g is really (g(x) - gbar(x))^2/2 from -1 to 1.

Take the average of these integrals to get your variance.

I'm not getting the answer so clearly my logic is wrong. Can anybody point me in the right direction?

 dtyrp 05-03-2017 10:08 PM

Re: *ANSWER* Questions 4-6 of Hwk 4 (bias and variance)

Wow major misunderstanding/typo. The pdf of a uniform random variable from -1 to 1 is 1/2 (i.e. 1/1--1). The expected value is 1/2*(a+b) or 1/2*0, or just zero. Anyway, so adding the uniform pdf p(x) into the integral just halves the value of each integral. Still not understanding what is wrong with my logic, though.

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