# CS446: Machine Learning

## Quiz 2

1. The boolean function (x1 OR x3 OR x4) over the boolean variables x1, x2, x3, x4 is a linear function over these variables. Which of the following is a correct "linear" representation for it?
1. x1 + x2 + x3 + x4 = 3
2. x1 + x2 + x3 + x4 >= 1
3. x1 + x3 + x4 >= 1
4. x1 + x3 + x4 = 1

2. Last quiz, we discussed a learning problem over n binary features, and our hypothesis space consisted of all conjunctions of size exactly k of these features, taking the form xi1 ^ xi2 ^ ... ^ xik, where i1, ..., ik ∈ {1, 2, ..., n}. This is known as the set of monotone conjunctions of size k.

Now we consider a slightly different hypothesis space. This new hypothesis space still consists of the conjunction of exactly k terms; however, each term can now consist of either a feature or its negation. That is, hypotheses are of the form zi1 ^ zi2 ^ ... ^ zik, where i1, ..., ik ∈ {1, 2, ..., n} and zij ∈ {xij, ¬xij}. Call this the set of all conjunctions of size k.

What is the size of our new hypothesis space relative to the size of the hypothesis space consisting of monotone conjunctions?
1. They have the same size
2. The new hypothesis space has a larger size
3. The new hypothesis space has a smaller size
4. Cannot be decided

3. Which of these is NOT an example of a binary classification task?
1. Predict whether an incoming email is spam or not spam.
2. Predict what number a handwritten digit represents (in {0, 1, 2, ..., 9})
3. Predict whether a book review is positive or negative
4. Predict whether or not an ad is relevant to a webpage

4. Which of these is NOT an example of supervised learning?

1. From sentences whose words are labeled with their part-of-speech tags, learn to predict the part-of-speech tags of the words in a sentence.
2. From images of animals labeled with the animal's name, learn to predict what animal is pictured in an image.
3. From sentences whose words are labeled with their part-of-speech tags, learn to predict the grammatical structure of a sentence.
4. From emails labeled as spam/not spam, learn to predict whether or not an e-mail is spam.

Dan Roth