# CS446: Machine Learning

## Quiz 1

1. The matrix A of order n is nonsingular if?
1. The determinant of A is nonzero
2. The rows and columns of A are linearly independent
3. Both (a) and (b) are true
4. Neither (a) nor (b) are true

2. When formulating the badges game as a machine learning problem, what could be an example of a boolean feature?
1. The data point "Dan Roth"
2. The second letter of a given name is equal to 'b'
3. The label of the name is '+'
4. A function assigning the '+' label to all names starting with the letter 'G'

3. Match the following terms to their definitions:
Terms:
1. Hypothesis space
2. Label space
3. Loss function
4. Instance space
Definitions:
1. The set of all functions that are being considered by the learning algorithm.
2. The set of possible outputs produced by the machine learning system (defined by the learning task).
3. The measure of success of a learner.
4. The set of all inputs given to a machine learning system (defined by the feature extraction process).

4. Which one of the following candidate hypotheses is consistent with the given training data?

 x1 x2 x3 x4 y 1 0 0 1 0 1 1 0 1 1 0 0 0 1 0 0 1 0 0 0 1 1 1 1 1
1. y = x1 ^ x2 ^ x3
2. y = x2 ^ x4
3. y = x4
4. y = x1 ^ x4

5. Assume that we have a learning problem over n binary features, and our hypothesis space consists of all conjunctions of up to size k (k < n). That is, each function in the hypothesis space is of the form xi1 ^ xi2 ^ ... ^ xik, where i1, ..., ik ∈ {1, 2, ..., n}.
What is the tightest upper bound on the size of our hypothesis space?
1. O(n)
2. O(nk)
3. O(nn)
4. O(kn)
5. O(kk)
6. O(k)

Dan Roth