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My understanding is that the Perceptron Learning Algorithm:

  • will not converge if the data is not linearly separable.
  • might take exponentially many iterations, even if the data is linearly separable.

I'm wondering if, after $k$ steps, anything can be said about the probability that the data is linearly separable?

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  • $\begingroup$ Interesting thought, but my hunch is you'll probably have to make some fairly strong assumptions on the distribution of the training data to say anything like this. $\endgroup$ – Dougal Jul 29 '15 at 18:03

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