1. The Naive Bayes Classifier Application to Text Classification Example: spam filtering Kunstmatige Intelligentie / RuG Marius Bulacu

2. 2 Bayes Formula Posterior probability of the class after seeing the data Prior probability of the class before seeing anything Unconditional probability of the data Conditional Likelihood of the data given the class

3. 3 Medical example p(+disease) = 0.002 p(+test | +disease) = 0.97 p(+test | -disease) = 0.04 p(+disease | +test) = p(+test | +disease) * p(+disease) / p(+test) = 0.97 * 0.002 / 0.04186 = 0.00194 / 0.04186 = 0.046 p(-disease | +test) = p(+test | -disease) * p(-disease) / p(+test) = 0.04 * 0.998 / 0.04186 = 0.03992 / 0.04186 = 0.953 p(+test) = p(+test | +disease) * p(+disease) + p(+test | -disease) * p(-disease) = 0.97 * 0.002 + 0.04 * 0.97 = 0.00194 + 0.03992 = 0.04186

4. 4 Accumulation of evidence “naive” assumption that X and Y are independent

5. 5 Spam filtering From acd@essex.ac.uk Mon Nov 10 19:23:44 2003 Return-Path: Received: from serlinux15.essex.ac.uk (serlinux15.essex.ac.uk [155.245.48.17]) by tcw2.ppsw.rug.nl (8.12.8/8.12.8) with ESMTP id hAAIecHC008727; Mon, 10 Nov 2003 19:40:38 +0100 Apologies for multiple postings. > 2nd C a l l f o r P a p e r s > > DAS 2004 > > Sixth IAPR International Workshop on > Document Analysis Systems > > September 8-10, 2004 > > Florence, Italy > > http://www.dsi.unifi.it/DAS04 > > Note: > There are two main additions with respect to the previous CFP: > 1) DAS&DL data are now available on the workshop web site > 2) Proceedings will be published by Springer Verlag in LNCS series Example of regular mail:

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8. 8 Learning to classify e-mail  Target concept Spam?: e-mail --> {-,+}  Each word represents an attribute characterizing the e-mail  Estimate p(+spam) and p(-spam) from the training data as well as the conditional likelihoods for all the encountered words  For a new e-mail, assuming naive Bayes conditional independence, compute the MAP hypothesis

9. 9 Conclusions  Effective: about 90% correct classification  Could be applied to any text classification problem  Needs to be polished