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# System prepended metadata

title: HTML2021 HW2 Grading Policy

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# HTML2021 HW2 Grading Policy

## p5

You will get points if you demonstrate you understand what  $d_{vc}$ is:
+ listing each $N$, until you find an $N$ that can't be shattered
+ Proving formally by finding the upper and lower bound of $d_{vc}$

Each option (a, b, c, d) is worth 5 points:
+ For ( c ):
    + As long as you prove by the above methods, I won't be too harsh on you
+ For ( a ), ( b ), and ( d ):
    + Many Students just wrote $\bigcirc\times\bigcirc\times\bigcirc$ or drew a graph without explanations. For each option, they were deducted by 5 points
    + Some students claim they found the breakpoint. However, they only found an $N$ that couldn't be shattered. They would be deducted by 5 points since they did not prove the situation for $N - 1, N-2...$


$\ast$Note:
+ Some of you did not prove by the above methods, but your explanation convinces me you understand the concept. I still gave you points
+ Some handwritings were unreadable for me. Please write clearly next time so the TAs can understand
+ Some students have all options correct, however there was no proof or the proof was too unformal, they were deducted by 10 points


## P7

20%

- Correct. Your answer and derivation is correct. Proof sketch: indicate two Hoeffding inequalities $P[|E_{in}(g) - E_{out}(g)| \le \epsilon ] \ge 1-\delta$ and $P[|E_{in}(g_\star) - E_{in}(g_\star)| \le \epsilon ] \ge 1-\delta$ with $\epsilon = \sqrt{\frac{1}{2N}\ln (\frac{2M}{\delta})}$  (with probability $1-\delta$). Moreover, make use of $E_{in}(g) \le E_{in}(g_\star)$ or equivalent inequality to derive the desired upper bound.

15%


- Almost correct: demonstrated an almost correct derivation but there is a minor error or skipped reasoning between steps.
    - e.g. unclear whether you make use of the property $E_{in}(g) \le E_{in}(g_\star)$.
    - e.g. minor error on E_in: $E_{in}(g) \approx E_{in}(g_\star)$ or "very small" or ambiguous drawings.

10%


- Partially correct: a sensible derivation is given, but there are some errors or skipped reasoning between steps.
    - e.g. error in using Hoeffding inequality.
    - e.g. plug g and g* directly into the bound of $h$ and conclude the bound.
    - e.g. make use of other incorrect or unrelated inequalities.

5%

- Good direction: Hoeffding for both hypothesis $g, g_\star$ is stated or some sensible efforts are shown, but the remaining derivation is incorrect.

0%


- The derivation is unclear or unrelated.

## P11

**Correct option: \(c\)**

There're 2 cases in this problem:

### Choose the correct option

We'll only check your explanations for the option \(c\).

**20 points:**

- Choosing the correct answer, explain it in a reasonable way.

- There are 2 cases that are not that correct, but points wouldn't be deducted
    - Claim that $XX^\dagger$ is a matrix where the elements in diagonal are either 0 or 1.
        $\to$ It's actually wrong, check the example: `X = [1 0 0; 1 0 0]`
    - Claim that the options will hold only when $X$ has full rank
    $\to$ Not that precise, you should specify: **full row rank**. check the example: `X = [1 2; 1 0; 0 0]`
    
**15 points**:
- Choosing the correct answer, but the explanation is unclear, or there's a minor mistake.
    - e.g., the option will hold only when X is invertible.
    $\to$ Wrong, check the example: `X = [1 0]`
    
**10 points:** Explanations are totally wrong, or it doesn't make sense at all.

**0 points:** Without explanations.

### Choose the incorrect option

If choosing an incorrect option, I'll grade your explanations to other choices, in order to give you partial points.

From (a). to (d)., each option worth 5 points, since you've chosen a wrong answer, you'll at most get 15 points.

## p12
### -0
Totally correct
### -5
Any typo, get -5.
### -10
Wrong $\nabla$. If you didn't show $\nabla$, you need to say this problem's likelihood is equivalent to the linear regression problem.
### -10
Correct answer, but your liklihood function reduction progress are uncorrect or have any error.
### -10
If you only say this problem is equivalent to the linear regression problem but no any proof or explaination. 
### -20
Wrong answer or no explanation.