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Since NB is a generative classifier, we assume that the data points are all generated from a distribution, right?

But since we can compute the MLE of p(x_i|y) by counting (MLE of p(x_i|y) = # of (x_i,y) / # of y), do we really need a specific distribution, if at all, to model the likelihood(p(x_i|y))?

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  • $\begingroup$ What about a test document that has no similar training points? Clearly you need a representative training set. $\endgroup$ – paparazzo Nov 6 '15 at 20:51
  • $\begingroup$ I don't quite follow the question. Naive Bayes is simply a concept of breaking the conditional probability due to independence. It's distribution independent. You can do it with our MLE if you wish. $\endgroup$ – SmallChess Nov 7 '15 at 2:54
  • $\begingroup$ Yes it's distribution independent. But we may need to assume a distribution to perform MLE. The distribution can be any arbitrary distribution, though. $\endgroup$ – AsymTrick Nov 7 '15 at 22:24
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The most harrowing problem would be "interpolation". That is, computing $p(x_i | y)$ for $x_i$ and $y$ you have not yet observed, but fall within the convex hull of your observations.

You have to bin events together, or come up with a wacky interpolation scheme. This does work. However, If you assume a distribution, $p(x_i | y)$ becomes continuous, and you end up with a more statisically sound means of interpolation.

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