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Old 01-09-2013, 01:00 PM
Anne Paulson Anne Paulson is offline
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Join Date: Jan 2013
Location: Silicon Valley
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Question PLA: Is randomly selecting the update important?

The official description of the perceptron learning algorithm says that we randomly select an incorrectly classified point, and then update to nudge that point closer to being correctly classified.

If we actually randomly select the next point from the uniform distribution of misclassified points, we're going to have to do a lot of annoying bookkeeping, because every single time we update, we'll have to recheck every single point, figure out which ones are now misclassified (remembering that a previously correctly classified point can now be misclassified after update), and randomly pick one of the bad points for the next update.

Now, obviously, if the PLA is going to converge, it will converge no matter how we pick the next misclassified point, as long as we eventually get to every misclassified point. How much difference does it make if we select our update points non-randomly? I'll do the random update for the homework, just in case it makes a difference, but I suspect it doesn't on average.
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