Machine Learning Spring 2015
Solution Assignment 01
Max Marks: 55
Theory Component
1 Hypothesis Spaces
1.1 Question 1 (10 points)
1. Consider the origin of the square is point (a, b) and the side-length of the square is s, then:
h(x) = (+1 (a≤x1≤a+s)AND(b≤x2≤b+s)
−1otherwise (1)
2. There are three parameters, a, b, s.
3. O(N3). There are three parameters, each can vary between (1, N).
4. The most general hypothesis will be one with paramters: a= 0, b = 0, s =N. There are
multiple hypotheses which can be considered most specific, all with parameter s= 1,0≤
a≤N, 0≤b≤N.
5. An axis aligned rectangle hypothesis would require 4 parameters, a, b, l, w, where (a, b) is
the origin of rectangle and l, w are the length and width of the rectangle, respectively.
An axis-aligned square hypothesis space is a special case of axis-aligned rectangles with
l=w=s. Therefore, every hypothesis that can be represented by axis-aligned squares can
be represented by axis-aligned rectangles as well but the vice-versa is not true. Therefore,
axis-aligned rectangle hypothesis is richer than axis-aligned squares.
2 Similarity measures
2.1 Question 2 (2 points)
1. Edit distance
2. Hamming distance
3. Jaccard distance
4. Cosine distance
Last 3 require our non-numeric data to be encoded either as sets or using 1-of-m encoding.
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