1. [4 points] Intro to Machine Learning
Consider the task of classifying an image as one of a set of objects. Suppose we use a convolutional neural network to do so (you will learn what this is later in the semester).
(a) For this setup, what is the data (often referred to as x(i))?
Your answer:
(b) For this setup, what is the label (often referred to as y(i))?
Your answer:
(c) For this setup, what is the model?
Your answer:
(d) What is the distinction between inference and learning for this task?
Your answer:
2. [8 points] K -Nearest Neighbors
K-Nearest Neighbors is an extension of the Nearest-Neighbor classification algorithm. Given a set of points with assigned labels, a new point is classified by considering the K points closest to it (according to some metric) and selecting the most common label among these points. One common metric to use for KNN is the squared euclidean distance, i.e.
2
d(x(1) , x(2) ) = kx(1) − x(2) k2 (1)
For this problem, consider the following set of points in R2, each of which is assigned with a label y ∈ {1, 2}:
x1
x2
y
1
0.4
−2.8
3.2
−1.3
−3
1
5.2
−1.1
1.4
3.2
3.1
2
1
2
1
1
2
(a) Classify each of the following points using the Nearest Neighbor rule (i.e. K = 1) with the squared euclidean distance metric.
x1
x2
y
−2.6
1.4
−2.5
6.6
1.6
1.2
?
?
?
Your answer:
(b) Classify each of the following points using the 3-Nearest Neighbor rule with the squared euclidean distance metric.
x1
x2
y
−2.6
1.4
−2.5
6.6
1.6
1.2
?
?
?
Your answer:
(c) Given a dataset containing n points, what is the outcome of classifying any additional point using the n-Nearest Neighbors algorithm?
Your answer:
(d) How many parameters are learned when applying K -nearest neighbors?
Your answer:
2
