# 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.