HW4 is out (due Friday, March 19)

[Mladen Kolar]

Homework 4 is out. [link http://www.cs.cmu.edu/~10702/Materials/a4.pdf]

It is due 3.00pm on Friday, March 19.

You can solve any three (out of four) problems in this homework. Please, CLEARLY mark which ones you want to be graded.

Although the homework is due in more than three weeks, it would be very beneficial for your success on the midterm if you started working on the homework early. 

Start early!

[Antonio Juarez]

Hello all:

For homework 4, I'm a little unclear on some details:

• Q1: Where we're estimating the s-th derivative of a function with kernel density estimation, a term \hat{p}_{n,s}(x) is mentioned. However, to be consistent with the notation in the notes, shouldn't this be \hat{p}_{h,s}(x) (Switch "n" for "h")?
• Q1, part b): shouldn't the inner exponent on the right side of the inequality be 2s+1? I obtained this result and it worked well for part c), which makes me think that 2s-1 is not the correct exponent.
• Q1, part d): What is the orthonormal Legendre basis on [−1, 1]?
• Q2: Where it says "Assume that f can be represented as...", a Phi symbol is used, but it's different from the phi used to represent the orthonormal trigonometric basis. Just to confirm, are these the same?
• Q2, part a): Where we're asked to prove that a certain expression is \delta_{jk}, what is \delta_{jk}? Are we only supposed to prove that the result is finite?

Antonio

[Mladen Kolar]

• Q1: Where we're estimating the s-th derivative of a function with kernel density estimation, a term \hat{p}_{n,s}(x) is mentioned. However, to be consistent with the notation in the notes, shouldn't this be \hat{p}_{h,s}(x) (Switch "n" for "h")?

I don't have the notes in front of me, but you are most likely correct.

• Q1, part b): shouldn't the inner exponent on the right side of the inequality be 2s+1? I obtained this result and it worked well for part c), which makes me think that 2s-1 is not the correct exponent.

Absolutely. The 2s-1 is indeed 2s+1. The homework has been updated.  Thanks for finding this bug.

• Q1, part d): What is the orthonormal Legendre basis on [−1, 1]?

I have updated the HW assignment with the definition of the orthonormal Legendre basis.

• Q2: Where it says "Assume that f can be represented as...", a Phi symbol is used, but it's different from the phi used to represent the orthonormal trigonometric basis. Just to confirm, are these the same?

This is a typo.  It is updated now.

• Q2, part a): Where we're asked to prove that a certain expression is \delta_{jk}, what is \delta_{jk}? Are we only supposed to prove that the result is finite?

\delta_{jk} is the Kronecker delta, i.e., it is equal to 1 when j = k, and 0 otherwise

[Antonio Juarez]

Hello all:

Does someone know whether the normal-CDF symbol used on question 3 to describe an alternate form for G(x) is the usual CDF of the normal with mean 0 and variance 1 or the CDF of the normal with mean 0 and variance \sigma^2? I'm having a hard time computing the limiting variance if the case is the former.

Antonio