# HTML 2021 HW3 Grading Policy

## P5

- Option 1: Using Hoeffding inequality.
- -1 points if there is a minor mistake, e.g. notation error
- -3 points if there is a major mistake or unclear derivation, e.g. error in using Hoeffding
- -5 points if the derivation of option 1 is unrelated or incorrect.
- Option 2: You should either (a) mention the likelihood is proportional to $\prod \mu^{y_i} (1-\mu)^{1-y_i}$ and take partial derivative to maximize it , or (b) mention Binomial distribution, or \(c\) mention the equivalence to option 4.
- -1 points if there is a minor mistake, e.g. notation error, only mention Bernoulli.
- -3 points if there is a major mistake or the derivation is unclear, e.g. likelihood function is wrong , "by statistics", "$\nu$ is mean so maximize", “by definition” ...
- -5 points if the derivation of option 2 is unrelated or incorrect.
- Option 3: You should take partial derivative to show it minimize the squared error.
- -1 points if there is a minor mistake.
- -3 points if there is a major mistake or unclear derivation, e.g. use simulation, ...
- -5 points if the derivation of option 3 is unrelated or incorrect.
- Option 4: You should either (a) take partial derivative to show it minimize the error, or (b) mention the equivalence to option 2
- -1 points if there is a minor mistake.
- -3 points if there is a major mistake or unclear derivation, e.g. "mean will minimize", ...
- -5 points if the derivation of option 4 is unrelated or incorrect.
## P7
- 20 Points
- Correct answer, your steps need clear and are necessary.
- 10 Points
- Almost correct, for example, you didn't show $V = - \nabla_{err}$ in detail or you didn't show how you caculate it.
- 5 Points
- Correct answer but you use excultion to choose the answer.
- 0 Points
- Wrong answer
## P9
- 20 Points
- The steps are totally correct regardless of your final answer choice. An example solution would be like writing down both $\textbf{w}_{\text{LIN}}$ and $\tilde{\textbf{w}}$, and derive the answer by comparing these two weights.
- 15 Points
- The steps are almost correct, but with some minor mistakes. (1) Making mistakes on matrix multiplication, such as $(AB)^{-1}=A^{-1}B^{-1}$ or $(AB)^{T}=A^{T}B^{T}$.
- 10 Points
- The solution includes one major mistake, but some part of it is reasonable. (1) Assuming $\textbf{X}$ is invertible. (2) Transformed data is not in the form of $\textbf{X}\Gamma^T$. (3) Assuming that there exists a $\textbf{w}$ such that $\textbf{X}\textbf{w}=\textbf{y}$. (4) Serious mistakes on matrix multiplication.
- 10 Points
- The answer is simulated by a program.
- 0 Point
- The solution is incorrect or includes more than 1 major mistakes. (1) Assuming $\textbf{X}$ is invertible. (2) Transformed data is not in the form of $\textbf{X}\Gamma^T$. (3) Assuming that there exists a $\textbf{w}$ such that $\textbf{X}\textbf{w}=\textbf{y}$. (4) Serious mistakes on matrix multiplication.

## P11

**Correct answer: \(c\)**

Basically, there're 3 cases:
- 20 Points
- Choosing the correct answer

- 10 Points
- Choosing (a), (b)
- The bounds are not tight enough.

- 5 Points
- Choosing (d), (e)
- We can find a counter-example to show that (d), (e) cannot upper-bound the given term.

Exceptions

- 15 Points
- Choosing the correct answer, with a minor issue.

- 10 Points
- Choosing the correct answer, with only high-level intuition / unreasonable explanation.

- 0 Points
- Totally unrelated / unreasonable explanations
- Without explanations