Bayesian filtering is based on the principle that most events are dependent and that the probability of an event occurring in the future can be inferred from the previous occurrences of that event. (More information about the mathematical basis of Bayesian filtering is available at Bayesian Parameter Estimation and An Introduction to Bayesian Networks and their Contemporary Applications)
(http://www-ccrma.stanford.edu/~jos/bayes/Bayesian_Parameter_Estimation.html
& http://www.niedermayer.ca/papers/bayesian/bayes.html.)

This same technique can be used to classify spam. If some piece of text occurs often in spam but not in legitimate mail, then it would be reasonable to assume that this email is probably spam.

Creating a tailor-made Bayesian word database

Before mail can be filtered using this method, the user needs to generate a database with words and tokens (such as the $ sign, IP addresses and domains, and so on), collected from a sample of spam mail and valid mail (referred to as ‘ham’).

A probability value is then assigned to each word or token; the probability is based on calculations that take into account how often that word occurs in spam as opposed to legitimate mail (ham). This is done by analyzing the users' outbound mail and by analyzing known spam: All the words and tokens in both pools of mail are analyzed to generate the probability that a particular word points to the mail being spam.

This word probability is calculated as follows: If the word "mortgage" occurs in 400 of 3,000 spam mails and in 5 out of 300 legitimate emails, for example, then its spam probability would be 0.8889 (that is, [400/3000] divided by [5/300 + 400/3000]).

Creating the ham database (tailored to Keystone)

It is important to note that the analysis of ham mail is performed on Keystone's mail, and is therefore tailored to Keystone. For example, a financial institution might use the word "mortgage" many times over and would get a lot of false positives if using a general anti spam rule set. On the other hand, the Bayesian filter, if tailored to Keystone School through an initial training period, takes note of Keystone's valid outbound mail (and recognizes "mortgage" as being frequently used in legitimate messages), it will have a much better spam detection rate and a far lower false positive rate.

NOTE: Some anti spam software with very basic Bayesian capabilities, such as the Outlook spam filter or the Internet Message Filter in Exchange Server, does not create a tailored ham data file for your company, but ships a standard ham data file with the installation. Although this method does not require an initial learning period, it has 2 major flaws:

1. The ham data file is publicly available and can thus be hacked by professional spammers and therefore bypassed. If the ham data file is unique to your company, then hacking the ham data file is useless. For example, there are hacks available to bypass the Microsoft Outlook 2003 or Exchange Server spam filter. For more information about this, see Microsoft Outlook 2003 Spam Filter: Under the hood.

2. The ham data file is a general one, and thus not tailored to your company, it cannot be as effective and you will suffer from noticeably higher false positives.

Creating the spam database

Besides ham mail, the Bayesian filter also relies on a spam data file. This spam data file must include a large sample of known spam and must be constantly updated with the latest spam by the anti spam software. This will ensure that the Bayesian filter is aware of the latest spam tricks, resulting in a high spam detection rate (NOTE: this is achieved once the required initial two-week learning period is over).

How the actual filtering is done

Once the ham and spam databases have been created, the word probabilities can be calculated and the filter is ready for use.
When a new mail arrives, it is broken down into words and the most relevant words - i.e., those that are most significant in identifying whether the mail is spam or not - are singled out. From these words, the Bayesian filter calculates the probability of the new message being spam or not. If the probability is greater than a threshold, say 0.9, then the message is classified as spam.

This Bayesian approach to spam is highly effective - a May 2003 BBC article reported that spam detection rates of over 99.7% can be achieved with a very low number of false positives!

Why Bayesian filtering is better

1. The Bayesian method takes the whole message into account - It recognizes keywords that identify spam, but it also recognizes words that denote valid mail. For example: not every email that contains the word "free" and "cash" is spam. The advantage of the Bayesian method is that it considers the most interesting words (as defined by their deviation from the mean) and comes up with a probability that a message is spam. The Bayesian method would find the words "cash" and "free" interesting but it would also recognize the name of the business contact who sent the message and thus classify the message as legitimate, for instance; it allows words to "balance" each other out. In other words, Bayesian filtering is a much more intelligent approach because it examines all aspects of a message, as opposed to keyword checking that classifies a mail as spam on the basis of a single word.

2. A Bayesian filter is constantly self-adapting - By learning from new spam and new valid outbound mails, the Bayesian filter evolves and adapts to new spam techniques. For example, when spammers started using "f-r-e-e" instead of "free" they succeeded in evading keyword checking until "f-r-e-e" was also included in the keyword database. On the other hand, the Bayesian filter automatically notices such tactics; in fact if the word "f-r-e-e" is found, it is an even better spam indicator, since it’s unlikely to occur in a ham mail. Another example would be using the word "5ex" instead of "Sex". You would probably not have a word 5ex in a ham mail, and therefore the likelihood that it is spam increases.

3. The Bayesian technique is sensitive to the user – It learns the email habits of the company and understands that, for example, the word ‘mortgage’ might indicate spam if the company running the filter is, say, a car dealership, whereas it would not indicate it as spam if the company is a financial institution dealing with mortgages.

4. The Bayesian method is multi-lingual and international - A Bayesian anti spam filter, being adaptive, can be used for any language required. Most keyword lists are available in English only and are therefore quite useless in non English-speaking regions. The Bayesian filter also takes into account certain language deviations or the diverse usage of certain words in different areas, even if the same language is spoken. This intelligence enables such a filter to catch more spam.

5. A Bayesian filter is difficult to fool, as opposed to a keyword filter - An advanced spammer who wants to trick a Bayesian filter can either use fewer words that usually indicate spam (such as free, Viagra, etc), or more words that generally indicate valid mail (such as a valid contact name, etc). Doing the latter is impossible because the spammer would have to know the email profile of each recipient - and a spammer can never hope to gather this kind of information from every intended recipient. Using neutral words, for example the word "public", would not work since these are disregarded in the final analysis. Breaking up words associated with spam, such as using "m-o-r-t-g-a-g-e" instead of "mortgage", will only increase the chance of the message being spam, since a legitimate user will rarely write the word "mortgage" as "m-o-r-t-g-a-g-e".

What’s the catch?

Bayesian filtering, if implemented the right way and tailored for Keystone is by far the most effective technology to combat spam. Is there a downside? There is one downside, but this can easily be overcome: Before you can use and judge the Bayesian filter, you have to wait for it to learn for at least two weeks - that or create the ham or spam databases yourself. This task can be quite complex, so it is best to wait until the filter has had time to learn. Over time, the Bayesian filter becomes more and more effective as it learns more about Keystone’s email habits. To quote the old saying, “Good things come to those who wait”.