Markovian discrimination

Markovian discrimination in spam filtering is a method used in CRM114 and other spam filters to model the statistical behaviors of spam and nonspam more accurately than in simple Bayesian methods. A simple Bayesian model of written text contains only the dictionary of legal words and their relative probabilities. A Markovian model adds the relative transition probabilities that given one word, predict what the next word will be. It is based on the theory of Markov chains by Andrey Markov, hence the name. In essence, a Bayesian filter works on single words alone, while a Markovian filter works on phrases or entire sentences.

There are two types of Markov models; the visible Markov model, and the hidden Markov model or HMM. The difference is that with a visible Markov model, the current word is considered to contain the entire state of the language model, while a hidden Markov model hides the state and presumes only that the current word is probabilistically related to the actual internal state of the language.

For example, in a visible Markov model the word "the" should predict with accuracy the following word, while in a hidden Markov model, the entire prior text implies the actual state and predicts the following words, but does not actually guarantee that state or prediction. Since the latter case is what's encountered in spam filtering, hidden Markov models are almost always used. In particular, because of storage limitations, the specific type of hidden Markov model called a Markov random field is particularly applicable, usually with a clique size of between four and six tokens.

References

• Chhabra, S., Yerazunis, W. S., and Siefkes, C. 2004. Spam Filtering using a Markov Random Field Model with Variable Weighting Schemas. In Proceedings of the Fourth IEEE international Conference on Data Mining (November 1 - 04, 2004). ICDM. IEEE Computer Society, Washington, DC, Mazharul