Paul Graham - Essays

I don't think this number can be trusted, partly because the sample is so small, and partly because I think I can fix the filter not to catch some of these.

False positives seem to me a different kind of error from false negatives. Filtering rate is a measure of performance. False positives I consider more like bugs. I approach improving the filtering rate as optimization, and decreasing false positives as debugging.

So these five false positives are my bug list. For example, the mail from Egypt got nailed because the uppercase text made it look to the filter like a Nigerian spam. This really is kind of a bug. As with html, the email being all uppercase is really conceptually one feature, not one for each word. I need to handle case in a more sophisticated way.

So what to make of this .06%? Not much, I think. You could treat it as an upper bound, bearing in mind the small sample size. But at this stage it is more a measure of the bugs in my implementation than some intrinsic false positive rate of Bayesian filtering.

What next? Filtering is an optimization problem, and the key to optimization is profiling. Don't try to guess where your code is slow, because you'll guess wrong. Look at where your code is slow, and fix that. In filtering, this translates to: look at the spams you miss, and figure out what you could have done to catch them.

For example, spammers are now working aggressively to evade filters, and one of the things they're doing is breaking up and misspelling words to prevent filters from recognizing them. But working on this is not my first priority, because I still have no trouble catching these spams [10].

There are two kinds of spams I currently do have trouble with. One is the type that pretends to be an email from a woman inviting you to go chat with her or see her profile on a dating site. These get through because they're the one type of sales pitch you can make without using sales talk. They use the same vocabulary as ordinary email.

The other kind of spams I have trouble filtering are those from companies in e.g. Bulgaria offering contract programming services. These get through because I'm a programmer too, and the spams are full of the same words as my real mail.

I'll probably focus on the personal ad type first. I think if I look closer I'll be able to find statistical differences between these and my real mail. The style of writing is certainly different, though it may take multiword filtering to catch that. Also, I notice they tend to repeat the url, and someone including a url in a legitimate mail wouldn't do that [11].

The outsourcing type are going to be hard to catch. Even if you sent a crawler to the site, you wouldn't find a smoking statistical gun. Maybe the only answer is a central list of domains advertised in spams [12]. But there can't be that many of this type of mail. If the only spams left were unsolicited offers of contract programming services from Bulgaria, we could all probably move on to working on something else.

Will statistical filtering actually get us to that point? I don't know. Right now, for me personally, spam is not a problem. But spammers haven't yet made a serious effort to spoof statistical filters. What will happen when they do?

I'm not optimistic about filters that work at the network level [13]. When there is a static obstacle worth getting past, spammers are pretty efficient at getting past it. There is already a company called Assurance Systems that will run your mail through Spamassassin and tell you whether it will get filtered out.

Network-level filters won't be completely useless. They may be enough to kill all the "opt-in" spam, meaning spam from companies like Virtumundo and Equalamail who claim that they're really running opt-in lists. You can filter those based just on the headers, no matter what they say in the body. But anyone willing to falsify headers or use open relays, presumably including most porn spammers, should be able to get some message past network-level filters if they want to. (By no means the message they'd like to send though, which is something.)

The kind of filters I'm optimistic about are ones that calculate probabilities based on each individual user's mail. These can be much more effective, not only in avoiding false positives, but in filtering too: for example, finding the recipient's email address base-64 encoded anywhere in a message is a very good spam indicator.

But the real advantage of individual filters is that they'll all be different. If everyone's filters have different probabilities, it will make the spammers' optimization loop, what programmers would call their edit-compile-test cycle, appallingly slow. Instead of just tweaking a spam till it gets through a copy of some filter they have on their desktop, they'll have to do a test mailing for each tweak. It would be like programming in a language without an interactive toplevel, and I wouldn't wish that on anyone.

[1] Paul Graham. ``A Plan for Spam.'' August 2002. http://paulgraham.com/spam.html.

Probabilities in this algorithm are calculated using a degenerate case of Bayes' Rule. There are two simplifying assumptions: that the probabilities of features (i.e. words) are independent, and that we know nothing about the prior probability of an email being spam.

The first assumption is widespread in text classification. Algorithms that use it are called ``naive Bayesian.''

The second assumption I made because the proportion of spam in my incoming mail fluctuated so much from day to day (indeed, from hour to hour) that the overall prior ratio seemed worthless as a predictor. If you assume that P(spam) and P(nonspam) are both .5, they cancel out and you can remove them from the formula.

If you were doing Bayesian filtering in a situation where the ratio of spam to nonspam was consistently very high or (especially) very low, you could probably improve filter performance by incorporating prior probabilities. To do this right you'd have to track ratios by time of day, because spam and legitimate mail volume both have distinct daily patterns.

[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'', ``$--.99'', and ``$--''.