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Old 07-02-2012, 02:13 PM
tadworthington tadworthington is offline
Join Date: Jun 2012
Location: Chicago, IL
Posts: 32
Default Re: Exercises and Problems

Problem 1.4

This is an excellent problem, and a model one in my opinion for helping a student to understand material. It starts out easy, with a small data set - that, importantly, is user-generated. Having to generate a data set - even one as simple as a linearly separable data set in 2 dimensions - goes a long way to helping understand how the Perceptron works and why it wouldn't work if the data were not linearly separable. We gradually progress to bigger data sets, all along the way plotting the data so that we can see what is happening. It is not only instructive but also quite exhilarating to see the results of the PLA (plotting both the target function and the hypothesis generated by the PLA) actually graphed out in front of you on a computer screen!

I also thought that the progression to 10 dimensions only after working through the more easily visualized 2 dimensional examples is perfect. Finally, the histogram approach to understanding the computational complexity of the PLA was, I thought, genius.

Overall I spent about 90 minutes on the problem, although a lot of that was spent documenting my code for future reference, and just general "prettying" of my plots and results; so I would guess that this problem can be completed comfortably in an hour, assuming knowledge of programming in a language where plotting is easy (I used Python, but Matlab/Octave would also be excellent examples for quick-and-dirty graphics programming of this type.) For someone with no programming experience, the problem would probably take much more time.

I think the problem is exceptionally clear.

I thought the problem was relatively easy, but the Perceptron is a relatively easy concept so I think making it harder is neither necessary nor appropriate. For metrics purposes, on a 1-10 scale of difficulty I would give this a 3.
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