1. Please read this statement and Agree/Disagree below:
“In submitting this assessment, I confirm that my conduct during this quiz adheres to the Code of Behaviour on Academic Matters. I confirm that I did NOT act in such a way that would constitute cheating, misrepresentation, or unfairness, including but not limited to, using unauthorized aids and assistance, impersonating another person, and committing plagiarism. I pledge upon my honour that I have not violated the Faculty of Applied Science & Engineering’s during this assessment.”
2. [2] We have that
𝑓(𝒙) = 𝑓(𝑥1, 𝑥2, 𝑥3) = 𝑙𝑛(𝑥1𝑥2) − 𝑥3 2
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𝑥1(𝑡) 𝑒𝑡 𝒙(𝑡) = [𝑥2(𝑡)] = [−𝑐𝑜𝑠(𝑡)]
Calculate the gradient 𝑑𝑓. Show all your calculations. 𝑑𝑡
3. [3] Binary classification Model A achieves a top F1 score of F1A and an area under the ROC curve (AUC) of AUCA, whereas binary classification Model B achieves a top F1 score of F1B and an AUC of AUCB, on the same dataset. If AUCA > AUCB., is it implied that F1A > F1B? Why?
4. [3] StandardScaler (in sklearn) is often used in linear regression models.
a. What does StandardScaler do?
b. Is it best practice to apply StandardScaler before or after splitting data into training and
testing groups? Why?
c. Typically, is it useful to apply StandardScaler on targets, feature data, or both?
5. [3] Sam applies linear regression to data that has a single feature, x. A first model, Model A,
makes predictions y using only a bias (𝑤0) and a weighted feature (𝑤1𝑥), i.e. 𝑦 = 𝑤0 + 𝑤1𝑥.
Unsatisfied, Sam then creates new features that are the x feature squared and cubed, yielding
the model 𝑦 = 𝑤 + 𝑤 𝑥 + 𝑤 𝑥2 + 𝑤 𝑥3 (Model B), which still isn’t a great fit. 012233
a. What minimum degree polynomial is needed to fit the data reasonably well? Why? [hint: count turning points (extremums) of polynomial]
b. Can you conceive of an alternate feature mapping scheme, where a single additional feature is added to Model A, that would fit the data well? Explain your reasoning.
6. [3] This term, several approaches to combat overfitting were discussed.
a. What is overfitting, and how do we know if a model is overfitted?
b. Describe two methods that are used to prevent overfitting. To what models do these
methods apply? (ie are they general, or specific to certain types of models?)
c. What are the major advantages and disadvantages of these methods?
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