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Exam Paper Ml

2270 words - 10 pages

MIDTERM: CS 6375
INSTRUCTOR: VIBHAV GOGATE
October, 23 2013

The exam is closed book. You are allowed a one-page cheat sheet. Answer the
questions in the spaces provided on the question sheets. If you run out of room for
an answer, use an additional sheet (available from the instructor) and staple it to
your exam.

• NAME

• UTD-ID if known

• SECTION 1:
• SECTION 2:
• SECTION 3:
• SECTION 4:
• SECTION 5:

• Out of 90:

1

CS 6375 FALL 2013

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CS 6375 FALL 2013

Midterm, Page 3 of 13

October 23, 2013

SECTION 1: SHORT QUESTIONS (15 points)
1. (3 points) The Naive Bayes classifier uses the maximum a posteriori or the ...view middle of the document...

The derivative of LL(θ) is:
−3

1
1
+6
1−θ

Setting it to zero and solving for θ, we get: θ = 1/2.

CS 6375 FALL 2013

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October 23, 2013

3. (2 points) If the data is not linearly separable, then the gradient descent algorithm for training
a logistic regression classifier will never converge. True or False. Explain your answer.
Solution: False. Our objective function is always concave. The algorithm will always converge
under mild assumptions.
4. (2 points) If the data is linearly separable, then the 3-nearest neighbors algorithm will always
have 100% accuracy on the training set. True or False. Explain your answer.
Solution: False. Here is the counter example.
X
Class

0.1
+

0.2
+

1
+

7

Here the data is linearly separable. However, the point (7, −) will be misclassified as + by the
3-nearest neighbors algorithm.
5. (2 points) The decision tree classifier has 100% accuracy on the training set (namely, the data
is noise-free). Will logistic regression have the same accuracy (100%) on the training set?
Solution: False. Decision tree can learn complex surfaces or Boolean functions (e.g., XOR).
However, logistic regression can only learn linear classification boundaries (e.g., it cannot represent XOR).

CS 6375 FALL 2013

Midterm, Page 5 of 13

October 23, 2013

SECTION 2: Decision Trees (20 points)
1. (4 points) Let x be a vector of n Boolean variables and let k be an integer less than n. Let fk
be a target concept which is a disjunction consisting of k literals.
(Let the n variables be denoted by the set {X1 , . . . , Xn }. Examples of f2 : X1 ∨ X2 , X1 ∨ ¬X4 ,
etc. Examples of f3 : X1 ∨ X2 ∨ X10 , X1 ∨ ¬X4 ∨ X7 , etc.)
State the size of the smallest possible consistent decision tree (namely a decision tree that
correctly classifies all possible examples) for fk in terms of n and k and describe its shape.
Solution: The smallest possible decision tree consistent withfk contains 2k + 1 nodes with k
internal nodes corresponding to the attributes and k + 1 leaf nodes. Each internal node (except
the node at depth k − 1 which has two leaf nodes) has one leaf node corresponding to an
assignment of true to the literal and has one child node corresponding to the false assignment
to the particular literal.
We wish to learn a decision tree to help students pick restaurants using three aspects – the
price, the location of the restaurant and the speed of service. The data for training the tree is
given below, where the target concept is the column labeled ”Like?”

2. (4 points) What is the entropy of the collection of examples with respect to the target label
(Like?) ?
Solution: We have 4 +ve and 4 −ve examples. Thus the entropy is 1.

CS 6375 FALL 2013

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October 23, 2013

SECTION 2: Decision Trees (20 points) — Continued
I have copied the dataset from the previous page to this page for convenience.

3. (4 points) Compute the...

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