Spam Filtering with Naive Bayes
Published July 27, 2018
19 min
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    Today's spam filters are advanced data driven tools. They rely on a variety of techniques to effectively and often seamlessly filter out junk email from good email.

    Whitelists, blacklists, traffic analysis, network analysis, and a variety of other tools are probably employed by most major players in this area. Naturally content analysis can be an especially powerful tool for detecting spam.

    Given the binary nature of the problem (Spam or \neg Spam) its clear that this is a great problem to use machine learning to solve. In order to apply machine learning, you first need a labelled training set. Thankfully, many standard corpora of labelled spam data are readily available. Further, if you're working for a company with a spam filtering problem, often asking users to self-moderate or flag things as spam can be an effective way to generate a large amount of labels for "free".

    With a labeled dataset in hand, a data scientist working on spam filtering must next do feature engineering. This should be done with consideration of the algorithm that will be used. The Naive Bayesian Classifer has been a popular choice for detecting spam because it tends to perform pretty well on high dimensional data, unlike a lot of other ML algorithms. It also is very efficient to compute, making it possible to train a per-user Classifier if one wished to. While we might do some basic NLP tricks, for the most part, we can turn each word in a document (or perhaps each bigram or n-gram in a document) into a feature.

    The Naive part of the Naive Bayesian Classifier stems from the naive assumption that all features in one's analysis are considered to be independent. If x and y are known to be independent, then Pr(x \cap y) = Pr(x) \cdot Pr(y). In other words, you just multiply the probabilities together. Shh, don't tell anyone, but this assumption is actually wrong! Certainly, if a document contains the word algorithm, it's more likely to contain the word probability than some randomly selected document. Thus, Pr(\text{algorithm} \cap \text{probability}) > Pr(\text{algorithm}) \cdot Pr(\text{probability}), violating the assumption. Despite this "flaw", the Naive Bayesian Classifier works remarkably will on many problems. If one employs the common approach of converting a document into bigrams (pairs of words instead of single words), then you can capture a good deal of this correlation indirectly.

    In the final leg of the discussion, we explore the question of whether or not a Naive Bayesian Classifier would be a good choice for detecting fake news.

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