VC Dimension - Carnegie Mellon School of Computer Science
Machine Learning: 10701 and 15781, 2003
Assignment 4
Primary contact for questions and clarifications: Rong Zhang (rongz@cs.cmu.edu)
Due Date: 10.30am Tuesday November 4th (one week)
Group Work: You may work in a group of two people if you wish.
1. VC Dimension (30 Points)
Consider the space of instance [pic] corresponding to all points in the 2D [pic] plane. Give the VC dimension of the following hypothesis spaces. No explanation required.
(a) [pic] = the set of all axes-parallel rectangles in the [pic] plane. That is, [pic]. Points inside the rectangle are classified as positive.
(b) [pic] = like (a), but including all rectangles (not just the ones parallel to the axes of coordinate system).
(c) [pic] = real-valued, depth-2 decision trees. For example, the following trees are in [pic].
x x
>=x0 / \ =x0 / \ =y0 / \ =y0 / \ =y1 / \ ................
................
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