[2] Patrick Pantel and Dekang Lin. ``SpamCop-- A Spam Classification & Organization Program.'' Proceedings of AAAI-98 Workshop on Learning for Text Categorization.
[3] Mehran Sahami, Susan Dumais, David Heckerman and Eric Horvitz. ``A Bayesian Approach to Filtering Junk E-Mail.'' Proceedings of AAAI-98 Workshop on Learning for Text Categorization.
[4] At the time I had zero false positives out of about 4,000 legitimate emails. If the next legitimate email was a false positive, this would give us .03%. These false positive rates are untrustworthy, as I explain later. I quote a number here only to emphasize that whatever the false positive rate is, it is less than 1.16%.
[5] Bill Yerazunis. ``Sparse Binary Polynomial Hash Message Filtering and The CRM114 Discriminator.'' Proceedings of 2003 Spam Conference.
[6] In ``A Plan for Spam'' I used thresholds of .99 and .01. It seems justifiable to use thresholds proportionate to the size of the corpora. Since I now have on the order of 10,000 of each type of mail, I use .9999 and .0001.
[7] There is a flaw here I should probably fix. Currently, when ``Subject*foo'' degenerates to just ``foo'', what that means is you're getting the stats for occurrences of ``foo'' in the body or header lines other than those I mark. What I should do is keep track of statistics for ``foo'' overall as well as specific versions, and degenerate from ``Subject*foo'' not to ``foo'' but to ``Anywhere*foo''. Ditto for case: I should degenerate from uppercase to any-case, not lowercase.
It would probably be a win to do this with prices too, e.g. to degenerate from ``$129.99'' to ``$--9.99'', ``$--.99'', and ``$--''.
You could also degenerate from words to their stems, but this would probably only improve filtering rates early on when you had small corpora.
[8] Steven Hauser. ``Statistical Spam Filter Works for Me.'' http://www.sofbot.com.
[9] False positives are not all equal, and we should remember this when comparing techniques for stopping spam. Whereas many of the false positives caused by filters will be near-spams that you wouldn't mind missing, false positives caused by blacklists, for example, will be just mail from people who chose the wrong ISP. In both cases you catch mail that's near spam, but for blacklists nearness is physical, and for filters it's textual.
[10] If spammers get good enough at obscuring tokens for this to be a problem, we can respond by simply removing whitespace, periods, commas, etc. and using a dictionary to pick the words out of the resulting sequence. And of course finding words this way that weren't visible in the original text would in itself be evidence of spam.
Picking out the words won't be trivial. It will require more than just reconstructing word boundaries; spammers both add (``xHot nPorn cSite'') and omit (``P#rn'') letters. Vision research may be useful here, since human vision is the limit that such tricks will approach.
[11] In general, spams are more repetitive than regular email. They want to pound that message home. I currently don't allow duplicates in the top 15 tokens, because you could get a false positive if the sender happens to use some bad word multiple times. (In my current filter, ``dick'' has a spam probabilty of .9999, but it's also a name.) It seems we should at least notice duplication though, so I may try allowing up to two of each token, as Brian Burton does in SpamProbe.
[12] This is what approaches like Brightmail's will degenerate into once spammers are pushed into using mad-lib techniques to generate everything else in the message.
[13] It's sometimes argued that we should be working on filtering at the network level, because it is more efficient. What people usually mean when they say this is: we currently filter at the network level, and we don't want to start over from scratch. But you can't dictate the problem to fit your solution.
Historically, scarce-resource arguments have been the losing side in debates about software design. People only tend to use them to justify choices (inaction in particular) made for other reasons.
Thanks to Sarah Harlin, Trevor Blackwell, and Dan Giffin for reading drafts of this paper, and to Dan again for most of the infrastructure that this filter runs on.
Why Nerds are Unpopular
When we were in junior high school, my friend Rich and I made a map of the school lunch tables according to popularity. This was easy to do, because kids only ate lunch with others of about the same popularity. We graded them from A to E. A tables were full of football players and cheerleaders and so on. E tables contained the kids with mild cases of Down's Syndrome, what in the language of the time we called "retards."
We sat at a D table, as low as you could get without looking physically different. We were not being especially candid to grade ourselves as D. It would have taken a deliberate lie to say otherwise. Everyone in the school knew exactly how popular everyone else was, including us.
My stock gradually rose during high school. Puberty finally arrived; I became a decent soccer player; I started a scandalous underground newspaper. So I've seen a good part of the popularity landscape.
I know a lot of people who were nerds in school, and they all tell the same story: there is a strong correlation between being smart and being a nerd, and an even stronger inverse correlation between being a nerd and being popular. Being smart seems to make you unpopular.
Why? To someone in school now, that may seem an odd question to ask. The mere fact is so overwhelming that it may seem strange to imagine that it could be any other way. But it could. Being smart doesn't make you an outcast in elementary school. Nor does it harm you in the real world. Nor, as far as I can tell, is the problem so bad in most other countries. But in a typical American secondary school, being smart is likely to make your life difficult. Why?
The key to this mystery is to rephrase the question slightly. Why don't smart kids make themselves popular? If they're so smart, why don't they figure out how popularity works and beat the system, just as they do for standardized tests?
One argument says that this would be impossible, that the smart kids are unpopular because the other kids envy them for being smart, and nothing they could do could make them popular. I wish. If the other kids in junior high school envied me, they did a great job of concealing it. And in any case, if being smart were really an enviable quality, the girls would have broken ranks. The guys that guys envy, girls like.
In the schools I went to, being smart just didn't matter much. Kids didn't admire it or despise it. All other things being equal, they would have preferred to be on the smart side of average rather than the dumb side, but intelligence counted far less than, say, physical appearance, charisma, or athletic ability.
So if intelligence in itself is not a factor in popularity, why are smart kids so consistently unpopular? The answer, I think, is that they don't really want to be popular.
If someone had told me that at the time, I would have laughed at him. Being unpopular in school makes kids miserable, some of them so miserable that they commit suicide. Telling me that I didn't want to be popular would have seemed like telling someone dying of thirst in a desert that he didn't want a glass of water. Of course I wanted to be popular.
But in fact I didn't, not enough. There was something else I wanted more: to be smart. Not simply to do well in school, though that counted for something, but to design beautiful rockets, or to write well, or to understand how to program computers. In general, to make great things.
At the time I never tried to separate my wants and weigh them against one another. If I had, I would have seen that being smart was more important. If someone had offered me the chance to be the most popular kid in school, but only at the price of being of average intelligence (humor me here), I wouldn't have taken it.