## CJ Korea Express:Opportunity in overhang

We believe CJ Korea Express saw its sales and operating profit rise a respective17.3% and 9.5% y-y in 3Q.

Question 1

The company on Oct 10said it would acquire the logistics and shipping units ofGemadept, Vietnam’s largest player, which shows that its M&A-focused strategy tobecome a global logistics leader remains on track.

Suppose that you have trained a logistic regression classifier, and it outputs on a new examplex a prediction hθ(x) = 0.7. This means (check all that apply):

The firm should continue to gain parcel delivery market share through year-end,while overall top-line growth will likely benefit from the additional consolidation ofsubsidiaries. Our BUY rating and 12-month target price of KRW220,000are bothunchanged.

Our estimate forP(y=1|x;θ) is 0.7.

Our estimate forP(y=0|x;θ) is 0.3.

Our estimate forP(y=1|x;θ) is 0.3.

Our estimate forP(y=0|x;θ) is 0.7.

Solution

Our estimate for P(y=1|x;θ) is 0.7. T hθ(x)is preciselyP(y=1|x;θ) , so each is 0.7. Our estimate for P(y=0|x;θ) is 0.3. T Since we must have P(y=0|x;θ) = 1−P(y=1|x;θ) , the former is 1−0.7=0.3 . Our estimate for P(y=1|x;θ) is 0.3. F hθ(x) gives P(y=1|x;θ) , not 1−P(y=1|x;θ) . Our estimate for P(y=0|x;θ) is 0.7. F hθ(x) is P(y=1|x;θ) , not P(y=0|x;θ)

Question2

Which of the following are true? Check all that apply.

1.  J(θ) will be a convex function, so gradient descent should converge to the global minimum.

2. CORRECT Adding polynomial features (e.g., instead using hθ(x)=g(θ0+θ1x1+θ2x2+θ3x21+θ4x1x2+θ5x22) ) could increase how well we can fit the training data.

3. The positive and negative examples cannot be separated using a straight line. So, gradient descent will fail to converge.

1. WRONG Because the positive and negative examples cannot be separated using a straight line, linear regression will perform as well as logistic regression on this data.

1,4 not correct

Question 3

For logistic regression, the gradient is given by ∂∂θjJ(θ)=1m∑mi=1(hθ(x(i))−y(i))x(i)j. Which of these is a correct gradient descent update for logistic regression with a learning rate of α? Check all that apply.

θ:=θ−α1m∑mi=1(θTx−y(i))x(i).

CORRECT θj:=θj−α1m∑mi=1(hθ(x(i))−y(i))x(i)j (simultaneously update for all j).

θj:=θj−α1m∑mi=1(hθ(x(i))−y(i))x(i) (simultaneously update for all j).

CORRECT θj:=θj−α1m∑mi=1(11+e−θTx(i)−y(i))x(i)j (simultaneously update for all j).

Suppose you have the following training set, and fit a logistic regression classifier hθ(x)=g(θ0+θ1x1+θ2x2) .

4.

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