Exercises and Problems

[yaser]

Please comment on the chapter problems in terms of difficulty, clarity, and time demands. This information will help us and other instructors in choosing problems to assign in our classes.

Also, please comment on the exercises in terms of how useful they are in understanding the material.

[jhmiller@tricity.wsu.edu]

How is values of Eout calculated in tables on page 121 that relate to Figure 4.1?

For the table referring to Figure 4.1a, I can see using the formula in Exercise 3.4e on page 88 if the value of sigma were known since d can be inferred from the degree of polynomial fit. I don't see that formula applying to values in the table that relate to Figure 4.1b because sigma is zero.

I can see using the formula for Eout in Exercise 3.4e on page 88 in Exercise 4.2 on page 123. Is this correct?

[yaser]

Originally Posted by jhmiller@tricity.wsu.edu

How is values of Eout calculated in tables on page 121 that relate to Figure 4.1?

For the table referring to Figure 4.1a, I can see using the formula in Exercise 3.4e on page 88 if the value of sigma were known since d can be inferred from the degree of polynomial fit. I don't see that formula applying to values in the table that relate to Figure 4.1b because sigma is zero.

I can see using the formula for Eout in Exercise 3.4e on page 88 in Exercise 4.2 on page 123. Is this correct?

Each part of Figure 4.1 illustrates a specific target and a specific training set. The value of in the table is calculated directly as the mean-squared error between this specific and the that resulted from fitting the training data shown. Later, we compute averages over targets and training sets in the more elaborate overfitting experiment.

[jhmiller@tricity.wsu.edu]

Thanks a million. I assume the mean square error between f and g is restricted to the range of x-values where training data exist. Is this correct?

[yaser]

Originally Posted by jhmiller@tricity.wsu.edu

Thanks a million. I assume the mean square error between f and g is restricted to the range of x-values where training data exist. Is this correct?

Correct, but the cause and effect is the other way around. The training data lies within the range of x-values where the mean-squared error is computed, namely the input space which is a finite range in this case.

[prithagupta.nsit]

For Exercise 4.4

I am not able to understand that in this exercise 4.4, what is actually w and do we have to consider the regularizatio also and if the formulae:
Ein(w) =1/N (Zwlin − y)T * (Zwlin − y)

how can w-wlin come in picture.
by this formula I am able to get the second term but not the second term?
Can anyone help me derive this expression or can anyone share his/her solution with me.

http://book.caltech.edu/bookforum/showthread.php?t=4512
same is the Ein used here??? is it out of sample error... I am not able to understand the conflict. What my understanding is that we have derived wlin but for a variable vector we first check how much does it vary from the wlin and multiplied by Z vector gives us how much function vary from average hypothesis and the second term gives us the error of Wlin predicting outputs. Is my understanding right??