QUESTIONS: 1)            Which of the following loss functions takes a value of exactly zero for sufficiently large margin? (Hint: see CIML chap 7 for the formal definition of all of these functions) (2 CORRECT ANSWERS SELECT BOTH)        Zero/one      Hinge      Logistic      Exponential      Squared   2) Consider the following data points, x1 = [−1,1], x2 = [0,2], x3 = [−1, −2], x4 = [2,0] with labels y1=y2=−1, y3=y4=1

QUESTIONS:

1)            Which of the following loss functions takes a value of exactly zero for sufficiently large margin? (Hint: see CIML chap 7 for the formal definition of all of these functions) (2 CORRECT ANSWERS SELECT BOTH)

Zero/one

Hinge

Logistic

Exponential

Squared

2) Consider the following data points, x1 = [−1,1], x2 = [0,2], x3 = [−1, −2], x4 = [2,0] with labels y1=y2=−1, y3=y4=1.  Given the weight vector and bias as following: w = (w1, w2)T= (1,−1)T, b=0. Calculate gradients with respect to different losses (round your answers to 4 digits after the decimal):

1. If you're estimating the bias of a coin that came up heads 10 times and tails 20 times, what is the maximum likelihood estimate for the bias of this coin (p(heads))? Round to the nearest 0.001.
2. Suppose X is a vector of 30 boolean attributes and Y is a single discrete-valued random variable that can take on 5 possible values. Let θ_ij=P(X_i|Y=y_j). What is the number of independent θ_ij parameters?
3. Assume you are using a Naive Bayes classifier to model P (Y|X₁, X₂), where all random variables are Boolean. What is the size of the weight vector w that represents the equivalent linear classifier?
4.  

1. The prediction of the classifier for X1 = 0, X2 = 0 is 0. What is the probability of the class?
2. The prediction for X1 = 0, X2 = 1 is 0. What is the probability of the class?
3. the prediction for X1 = 1, X2 = 0 is 0. What is the probability of the class?
4. What is the prediction for X1 = 1, X2 = 1 is 0. What is the probability of the class?
5. Consider the classifier trained in the previous questions. What is the expected error rate on any test examples generated using Tables 1 and 2?
6. Consider the same scenario as the previous questions, but without the duplicate feature X2. What is the expected error rate of the classifier in this case?