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A Plan for Spam



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August 2002(This article describes the spam-filtering techniques
used in the spamproof web-based mail reader we
built to exercise Arc. An
improved algorithm is described in Better
Bayesian Filtering.)I think it's possible to stop spam, and that 
content-based filters are the way to do it.
The Achilles heel of the spammers is their message.
They can circumvent any other barrier you set up.  They have so far, at
least.  But they have to deliver their message, whatever it
is.  If we can write software that recognizes their messages,
there is no way they can get around that._ _ _To the recipient, spam is easily recognizable.  If you hired 
someone to read your mail and discard the spam, they would
have little trouble doing it.  How much do we have
to do, short of AI, to automate this process?I think we will be able to solve the problem with fairly
simple algorithms.  In fact, I've found that you can filter
present-day spam acceptably well using nothing more than a
Bayesian combination of the spam probabilities of individual
words.  Using a slightly tweaked (as described below) Bayesian
filter, we now miss less than 5 per 1000 spams, with 0 false positives.The statistical approach is not usually the first one people
try when they write spam filters.  Most hackers' first instinct is
to try to write software that recognizes individual properties of
spam.  You look at spams
and you think, the gall of these guys to try sending me mail 
that begins "Dear Friend" or has a subject line that's all
uppercase and ends in eight exclamation points.  I can filter
out that stuff with about one line of code.And so you do,
and in the beginning it works.  A few simple rules will take
a big bite out of your incoming spam.  Merely looking
for the word "click" will catch 79.7% of the
emails in my spam corpus, with only 1.2% false positives.I spent about six months writing software that looked for
individual spam features before I tried the statistical
approach.  What I found was that recognizing that last few
percent of spams got very hard, and that as I
made the filters stricter I got more false positives.False positives are innocent emails that get mistakenly
identified as spams.
For most users,
missing legitimate email is
an order of magnitude worse than receiving spam, so a
filter that yields false positives is like an acne cure
that carries a risk of death to the patient.The more spam a user gets, the less
likely he'll be to notice one innocent mail sitting in his
spam folder.  And strangely enough, the better your spam filters get,
the more dangerous false positives become, because when the
filters are really good, users will be more likely to
ignore everything they catch.I don't know why I avoided trying the statistical approach
for so long.  I think it was because I got addicted to
trying to identify spam features myself, as if I were playing
some kind of competitive game with the spammers.  (Nonhackers
don't often realize this, but most hackers are very competitive.)
When I did try statistical analysis, I
found immediately that it was much cleverer than I had been.
It discovered, of course, that terms like "virtumundo" and
"teens" were good indicators of spam.  But it also
discovered that "per" and "FL" and "ff0000" are good 
indicators of spam.  In fact, "ff0000" (html for bright red)
turns out to be as good an indicator of spam as any  
pornographic term._ _ _Here's a sketch of how I do statistical filtering.  I start
with one corpus of spam and one of nonspam mail.  At the
moment each one has about 4000 messages in it.  I scan
the entire text, including headers and embedded html
and javascript, of each message in each corpus.
I currently consider alphanumeric characters,
dashes, apostrophes, and dollar signs to be part of tokens,
and everything else to be a token separator.  (There is
probably room for improvement here.)  I ignore tokens that
are all digits, and I also ignore html comments, not even
considering them as token separators.I count the number
of times each token (ignoring case, currently) occurs in
each corpus.  At this stage I end up with two large hash   
tables, one for each corpus, mapping tokens to number
of occurrences.Next I create a third hash table, this time mapping
each token to the probability that an email containing it is a spam,
which I calculate as follows [1]:

(let ((g (* 2 (or (gethash word good) 0)))
      (b (or (gethash word bad) 0)))
   (unless (< (+ g b) 5)
     (max .01
          (min .99 (float (/ (min 1 (/ b nbad))
                             (+ (min 1 (/ g ngood))   
                                (min 1 (/ b nbad)))))))))

where word is the token whose probability we're
calculating, good and bad are the hash tables
I created in the first step, and ngood and nbad
are the number of nonspam and spam messages respectively.I explained this as code to show a couple of important details.
I want to bias the probabilities slightly to avoid false
positives, and by trial and error I've found that a good
way to do it is to double all the numbers in good.
This helps to distinguish between words that occasionally
do occur in legitimate email and words that almost never do. 
I only consider words that occur more than five times in
total (actually, because of the doubling, occurring three 
times in nonspam mail would be enough).  And then there is
the question of what probability to assign to words that
occur in one corpus but not the other.  Again by trial and   
error I chose .01 and .99.  There may be room for tuning
here, but as the corpus grows such tuning will happen
automatically anyway.The especially observant will notice that while I consider
each corpus to be a single long stream of text for purposes
of counting occurrences, I use the number of emails in
each, rather than their combined length, as the divisor     
in calculating spam probabilities.  This adds another
slight bias to protect against false positives.When new mail arrives, it is scanned into tokens, and
the most interesting fifteen tokens, where interesting is  
measured by how far their spam probability is from a
neutral .5, are used to calculate the probability that
the mail is spam.  If probs
is a list of the fifteen individual probabilities, you
calculate the 
combined probability thus:

(let ((prod (apply #'* probs)))
  (/ prod (+ prod (apply #'* (mapcar #'(lambda (x) 
                                         (- 1 x))
                                     probs)))))

One question that arises in
practice is what probability to assign to a word you've
never seen, i.e. one that doesn't occur in the hash table
of word probabilities.  I've found, again by trial and
error, that .4 is a good number to use.  If you've never
seen a word before, it is probably fairly innocent; spam
words tend to be all too familiar.There are examples of this algorithm being applied to
actual emails in an appendix at the end.I treat mail as spam if the algorithm above gives it a
probability of more than .9 of being spam.  But in practice
it would not matter much where I put this threshold, because
few probabilities end up in the middle of the range._ _ _One great advantage of the statistical approach is that you
don't have to read so many spams.  Over the past six months,
I've read literally thousands of spams, and it is really
kind of demoralizing.  <NAME> said if you compete
with slaves you become a slave, and there is something
similarly degrading about competing with spammers.   To
recognize individual spam features you have to try to get
into the mind of the spammer, and frankly I want to spend
as little time inside the minds of spammers as possible.But the real advantage of the Bayesian approach, of course,
is that you know what
you're measuring.  Feature-recognizing filters like
SpamAssassin assign a spam "score" to email.  The Bayesian
approach assigns an actual probability.  The problem with
a "score" is that no one knows what it means.  The user
doesn't know what it means, but worse still, neither does
the developer of the filter.  How many points should an
email get for having the word "sex" in it?  A probability
can of course be mistaken, but there is little ambiguity
about what it means, or how evidence should be combined
to calculate it.  Based on my corpus, "sex" indicates
a .97 probability of the containing email being a spam,
whereas "sexy" indicates .99 probability.
And Bayes' Rule, equally unambiguous, says that an email
containing both words would, in the (unlikely)
absence of any other evidence, have a 99.97% chance of
being a spam.Because it is measuring probabilities, the Bayesian approach
considers all the evidence in the email, both good and bad.
Words that occur disproportionately rarely
in spam (like "though" or "tonight" or "apparently")
contribute as much to decreasing the probability as
bad words like "unsubscribe" and "opt-in" do to
increasing it.  So an otherwise innocent email that happens
to include the word "sex" is not going to get tagged as spam.Ideally, of course, the probabilities should be calculated
individually for each user.  I get a lot of email containing
the word "Lisp", and (so far) no spam that does.  So a word
like that is effectively a kind of password for sending
mail to me.  In my earlier spam-filtering software, the user
could set up a list of such words and mail containing
them would automatically get past the filters.  On my
list I put words like "Lisp" and also my zipcode, so
that (otherwise rather spammy-sounding) receipts from
online orders would get through.  I thought I was being
very clever, but I found that the Bayesian filter did the
same thing for me, and moreover discovered of a lot of words I
hadn't thought of.When I said at the start that our filters let through less than
5 spams per 1000 with 0 false positives, I'm talking about
filtering my mail based on a corpus of my mail.  But these
numbers are not misleading, because that is the approach I'm
advocating: filter each user's mail based on the spam and
nonspam mail he receives.  Essentially, each user should
have two delete buttons, ordinary delete and delete-as-spam.
Anything deleted as spam goes into the spam corpus,   
and everything else goes into the nonspam corpus.You could start
users with a seed filter, but ultimately each user should have
his own per-word probabilities based on the actual mail he
receives.  This (a) makes the filters more effective, (b) lets
each user decide their own precise definition of spam,
and (c) perhaps best of all makes it hard for spammers
to tune mails to get through the filters.  If a lot of the  
brain of the filter is in the individual databases, then 
merely tuning spams to get through the seed filters
won't guarantee anything about how well they'll get through
individual users' varying and much more trained filters.Content-based spam filtering is often combined with a whitelist,
a list of senders whose mail can be accepted with no filtering.
One easy way to build such a
whitelist is to keep a list of every address the user has
ever sent mail to.  If a mail reader has a delete-as-spam
button then you could also add the from address
of every email the user has deleted as ordinary trash.I'm an advocate of whitelists, but more as a way to save  
computation than as a way to improve filtering.  I used to think that
whitelists would make filtering easier, because you'd
only have to filter email from people you'd never heard
from, and someone sending you mail for the first time is
constrained by convention in what they can say to you.
Someone you already know might send you an email talking about sex,
but someone sending you mail for the first time would not   
be likely to.  The problem is, people can have more than one 
email address, so a new from-address doesn't guarantee that
the sender is writing to you for the first time.
It is not unusual
for an old friend (especially if he is a hacker) to suddenly
send you an email with a new from-address, so you can't
risk false positives by filtering mail from unknown  
addresses especially stringently.In a sense, though, my filters do themselves embody a kind
of whitelist (and blacklist) because they are based on
entire messages, including the headers.  So to that
extent they "know" the email addresses of trusted senders
and even the routes by which mail gets from them to me.   
And they know the same about spam, including the server   
names, mailer versions, and protocols._ _ _If I thought that I could keep up current rates of spam
filtering, I would consider this problem solved.  But it
doesn't mean much to be able to filter out most present-day
spam, because spam evolves.
Indeed, most 
antispam techniques so far have been like pesticides that
do nothing more than create a new, resistant strain of bugs.I'm more hopeful about Bayesian filters, because they evolve
with the spam.  So as spammers start using "c0ck"   
instead of "cock" to evade simple-minded spam filters     
based on individual words, Bayesian filters automatically
notice.  Indeed, "c0ck" is far more damning evidence than
"cock", and Bayesian filters know precisely how much more.Still, anyone who proposes a plan for spam filtering has to
be able to answer the question: if the spammers knew
exactly what you were doing,
how well could they get past you?  For example, I think that if
checksum-based spam filtering becomes a serious obstacle,
the spammers will just
switch to mad-lib techniques for generating message bodies.To beat Bayesian filters, it would not be enough for spammers
to make their emails unique or to stop using individual
naughty words.  They'd have to make their mails indistinguishable
from your ordinary mail.  And this I think would severely
constrain them.  Spam is mostly sales
pitches, so unless your regular mail is all sales pitches,
spams will inevitably have a different character.  And    
the spammers would also, of course, have to change (and keep 
changing) their whole infrastructure, because otherwise
the headers would look as bad to the Bayesian filters as ever,
no matter what they did to the message body.  I don't know
enough about the infrastructure that spammers use to know
how hard it would be to make the headers look innocent, but
my guess is that it would be even harder than making the    
message look innocent.Assuming they could solve the problem of the headers,
the spam of the future will probably look something like
this:

Hey there.  Thought you should check out the following:
http://www.27meg.com/foo

because that is about as much sales pitch as content-based
filtering will leave the spammer room to make.  (Indeed, it
will be hard even to get this past filters, because if everything
else in the email is neutral, the spam probability will hinge on
the url, and it will take some effort to make that look neutral.)Spammers range from businesses running so-called
opt-in lists who don't even try to conceal their identities,
to guys who hijack mail servers to send out spams promoting
porn sites.  If we use filtering to whittle their
options down to mails like the one above, that should
pretty much put the spammers on the "legitimate" end of
the spectrum out of business; they feel obliged
by various state laws to include boilerplate about why
their spam is not spam, and how to cancel your
"subscription,"  and that kind of text is easy to   
recognize.(I used to think it was naive to believe that stricter laws
would decrease spam.  Now I think that while stricter laws  
may not decrease the amount of spam that spammers send,
they can certainly help filters to decrease the amount of  
spam that recipients actually see.)All along the spectrum, if you restrict the sales pitches spammers
can make, you will inevitably tend to put them out of
business.  That word business is an important one to
remember.  The spammers are businessmen.  They send spam because
it works.  It works because although the response rate
is abominably low (at best 15 per million, vs 3000 per
million for a catalog mailing), the cost, to them, is  
practically nothing.  The cost is enormous for the recipients,   
about 5 man-weeks for each million recipients who spend  
a second to delete the spam, but the spammer
doesn't have to pay that.Sending spam does cost the spammer something, though. [2]
So the lower we can get the
response rate-- whether by filtering, or by using filters to force
spammers to dilute their pitches-- the fewer businesses will find it
worth their while to send spam.The reason the spammers use the kinds of 
sales
pitches that they do is to increase response rates.
This is possibly even more disgusting
than getting inside the mind of a spammer,
but let's take a quick look inside the mind of someone
who responds to a spam.  This person is either
astonishingly credulous or deeply in denial about their   
sexual interests.  In either case, repulsive or
idiotic as the spam seems to us, it is exciting
to them.  The spammers wouldn't say these things if they
didn't sound exciting.  And "thought you
should check out the following" is just not going to
have nearly the pull with the spam recipient as
the kinds of things that spammers say now.
Result: if it can't contain exciting sales pitches,
spam becomes less effective as a marketing vehicle,
and fewer businesses want to use it.That is the big win in the end.  I started writing spam
filtering software because I didn't want have to look at
the stuff anymore.
But if we get good enough at filtering
out spam, it will stop working, and the spammers
will actually stop sending it._ _ _Of all the approaches to fighting spam, from software to laws,
I believe Bayesian filtering will be the single most
effective.  But I also
think that the more different kinds of antispam efforts
we undertake, the better, because any measure that
constrains spammers will tend to make filtering easier.
And even within the world of content-based filtering, I think
it will be a good thing if there are many different kinds
of software being used simultaneously.  The more different 
filters there are, the harder it will be for
spammers to tune spams to get through them.
Appendix: Examples of FilteringHere is an example of a spam that arrived while I was writing
this article.  The fifteen most interesting words in this spam are:

qvp0045
indira
mx-05
intimail
$7500
freeyankeedom
cdo
bluefoxmedia
jpg
unsecured
platinum
3d0
qves
7c5
7c266675

The words are a mix of stuff from the headers and from the
message body, which is typical of spam.  Also typical of spam
is that every one of these words has a spam probability,
in my database, of .99.  In fact there are more than fifteen words
with probabilities of .99, and these are just the first
fifteen seen.Unfortunately that makes this email a boring example of
the use of Bayes' Rule.  To see an interesting variety of
probabilities we have to look at this actually quite
atypical spam.The fifteen most interesting words in this spam, with their probabilities,
are:

madam           0.99
promotion       0.99
republic        0.99
shortest        0.047225013
mandatory       0.047225013
standardization 0.07347802
sorry           0.08221981
supported       0.09019077
people's        0.09019077
enter           0.9075001
quality         0.8921298
organization    0.12454646
investment      0.8568143
very            0.14758544
valuable        0.82347786 

This time the evidence is a mix of good and bad.  A word like  
"shortest" is almost as much evidence for innocence as a
word like "madam" or "promotion" is for guilt.  But still the
case for guilt is stronger.  If you combine these numbers
according to Bayes' Rule, the resulting probability is .9027."Madam" is obviously from spams beginning
"Dear Sir or Madam."  They're not very common, but the
word "madam" never occurs in my legitimate email, and
it's all about the ratio."Republic" scores high because
it often shows up in Nigerian scam emails, and also occurs once
or twice in spams referring to Korea and South Africa.
You might say that it's
an accident that it thus helps identify this spam.  But I've
found when examining spam probabilities that there are
a lot of these accidents, and they have an uncanny tendency to
push things in the right direction rather than the wrong one.
In this case, it is not entirely a coincidence that the word
"Republic" occurs in Nigerian scam emails and this spam.
There is a whole class of dubious business propositions involving
less developed countries, and these in turn are more likely
to have names that specify explicitly (because they aren't) that they
are republics.[3]On the other hand, "enter" is a genuine miss.  It occurs
mostly in unsubscribe instructions, but here is used in a
completely innocent way.  Fortunately the statistical approach is
fairly robust, and can tolerate quite a lot of misses
before the results start to be thrown off.For comparison, 
here is an example of that rare bird, a spam that
gets through the filters.  Why?  Because by sheer chance it happens
to be loaded with words that occur in my actual email:

perl       0.01
python     0.01
tcl        0.01
scripting  0.01
morris     0.01
graham     0.01491078
guarantee  0.9762507
cgi        0.9734398
paul       0.027040077
quite      0.030676773
pop3       0.042199217
various    0.06080265
prices     0.9359873
managed    0.06451222
difficult  0.071706355

There are a couple pieces of good news here.  First, this mail
probably wouldn't get through the filters of someone who didn't
happen to specialize in programming languages and have a good
friend called Morris.  For the average user, all the top five words here 
would be neutral and would not contribute to the spam probability.Second, I think filtering based on word pairs 
(see below) might well
catch this one:  "cost effective", "setup fee", "money back" -- pretty
incriminating stuff.  And of course if they continued to spam me
(or a network I was part of), "Hostex" itself would be
recognized as  a spam term.Finally, here is an innocent email.
Its  fifteen most interesting words are as follows:

continuation  0.01
describe      0.01
continuations 0.01
example       0.033600237
programming   0.05214485 
i'm           0.055427782
examples      0.07972858 
color         0.9189189  
localhost     0.09883721
hi            0.116539136
california    0.84421706
same          0.15981844
spot          0.1654587
us-ascii      0.16804294
what          0.19212411

Most of the words here indicate the mail is an innocent one.
There are two bad smelling words,  "color"
(spammers love colored fonts) and "California"
(which occurs in testimonials and also in menus in
forms), but they are not enough to outweigh obviously
innocent words like "continuation" and "example".It's interesting that "describe" rates as so thoroughly
innocent.  It hasn't occurred in a
single one of my 4000 spams.  The data turns out to be
full of such surprises.  One of the things you learn
when you analyze spam texts is how
narrow a subset of the language spammers operate in.  It's
that fact, together with the equally characteristic vocabulary
of any individual user's mail, that makes Bayesian filtering
a good bet.Appendix: More IdeasOne idea that I haven't tried yet is to filter based on
word pairs, or even triples, rather than individual words.
This should yield a much sharper estimate of the probability.
For example, in my current database, the word "offers"
has a probability of .96.  If you based the probabilities  
on word pairs, you'd end up with "special offers"
and "valuable offers" having probabilities of .99
and, say, "approach offers" (as in "this approach offers")
having a probability of .1 or less.The reason I haven't done this is that filtering based on
individual words already works so well.  But it does
mean that there is room to tighten the filters if spam
gets harder to detect.
(Curiously, a filter based on word pairs would be
in effect a Markov-chaining text generator running
in reverse.)Specific spam features (e.g. not seeing the recipient's
address in the to: field) do of course have value in 
recognizing spam.  They can be considered in this
algorithm by treating them as virtual words.  I'll probably
do this in future versions, at least for a handful of the
most egregious spam indicators. Feature-recognizing
spam filters are right in many details; what they lack
is an overall discipline for combining evidence.Recognizing nonspam features may be more important than
recognizing spam features.  False positives are such a
worry that they demand extraordinary measures.  I will
probably in future versions add a second level of testing
designed specifically to avoid false positives.  If a
mail triggers this second level of filters it will be accepted
even if its spam probability is above the threshold.I don't expect this second level of filtering to be Bayesian.
It will inevitably 
be not only ad hoc, but based on guesses, because the number of
false positives will not tend to be large enough to notice patterns.
(It is just as well, anyway, if a backup system doesn't rely on the same
technology as the primary system.)Another thing I may try in the future is to focus extra attention
on specific parts of the email.  For example, about 95% of current
spam includes the url of a site they want
you to visit.  (The remaining 5% want you to call a phone number,
reply by email or to a US mail address, or in a few
cases to buy a certain stock.)   The url is in such cases
practically enough by itself to determine whether the email
is spam.Domain names differ from the rest of the text in
a (non-German) email in that they often consist of several
words stuck together.  Though computationally expensive 
in the general case, it might be worth trying to 
decompose them.  If a filter has never seen the
token "xxx<PASSWORD>" before it will have an individual spam
probability of .4, whereas "xxx" and "porn" individually
have probabilities (in my corpus) of .9889 and .99
respectively, and a combined probability of .9998.I expect decomposing domain names to become more
important as spammers are gradually forced to stop using
incriminating words in the text of their messages.  (A url
with an ip address is of course an extremely incriminating sign,
except in the mail of a few sysadmins.)It might be a good idea to have a cooperatively maintained
list of urls promoted by spammers.  We'd need a trust metric
of the type studied by <NAME> to prevent malicious
or incompetent submissions, but if we had such a thing it
would provide a boost to any filtering software.   It would
also be a convenient basis for boycotts.Another way to test dubious urls would be to send out a
crawler to look at the site before the user looked at the
email mentioning it.  You could use a Bayesian filter to
rate the site just as you would an email, and whatever
was found on the site could be included in calculating
the probability of the email being a spam.  A url that led
to a redirect would of course be especially suspicious.One cooperative project that I think really would be a good
idea would be to accumulate a giant corpus of spam.  A large,
clean corpus is the key to making Bayesian filtering work
well.  Bayesian filters could actually use the corpus as
input.  But such a corpus would be useful for other kinds
of filters too, because it could be used to test them.Creating such a corpus poses some technical problems.  We'd
need trust metrics to prevent malicious or incompetent
submissions, of course.  We'd also need ways of erasing   
personal information (not just to-addresses and ccs, but
also e.g. the arguments to unsubscribe urls, which often
encode the to-address) from mails in the corpus.  If anyone
wants to take on this project, it would be a good thing for
the world.Appendix: Defining SpamI think there is a rough
consensus on what spam is, but it would be useful to have
an explicit definition.  We'll need to do this if we want to establish
a central corpus of spam, or even to compare spam filtering
rates meaningfully.To start with, spam is not unsolicited commercial email.
If someone in my neighborhood heard that I was looking for an old
Raleigh three-speed in good condition, and sent me an email
offering to sell me one, I'd be delighted, and yet this
email would be both commercial and unsolicited.  The
defining feature of spam (in fact, its raison d'etre)
is not that it is unsolicited, but that it is automated.It is merely incidental, too, that spam is usually commercial.
If someone started sending mass email to support some political
cause, for example, it would be just as much spam as email
promoting a porn site.I propose we define spam as unsolicited automated email.
This definition thus includes some email
that many legal definitions of spam don't.  Legal definitions
of spam, influenced presumably by lobbyists, tend to exclude
mail sent by companies that have an "existing relationship" with
the recipient.  But buying something from a company, for
example, does not imply that you have solicited
ongoing email from them.
If I order something from an online
store, and they then send me a stream of spam, it's still
spam.Companies sending spam often give you a way to "unsubscribe,"
or ask you to go to their site and change your "account
preferences" if you want to stop getting spam.  This is
not enough to stop the mail from being spam.  Not opting out
is not the same as opting in.  Unless the   
recipient explicitly checked a clearly labelled box (whose
default was no) asking to receive the email, then it is spam.In some business relationships, you do implicitly solicit
certain kinds of mail.   When you order online, I think you
implicitly solicit a receipt, and notification when the
order ships.
I don't mind when Verisign sends me mail warning that
a domain name is about to expire (at least, if they are the
actual 
registrar for it).  But when Verisign sends me
email offering a FREE Guide to Building My
E-Commerce Web Site, that's spam.
Notes:[1] The examples in this article are translated
into Common Lisp for, believe it or not, greater accessibility.
The application described here is one that we wrote in order to
test a new Lisp dialect called Arc that is 
not yet released.[2] Currently the lowest rate seems to be about $200 to send a million spams.
That's very cheap, 1/50th of a cent per spam.
But filtering out 95%
of spam, for example, would increase the spammers' cost to reach
a given audience by a factor of 20.  Few can have
margins big enough to absorb that.[3] As a rule of thumb, the more qualifiers there are before the
name of a country, the more corrupt the rulers.  A
country called The Socialist People's Democratic Republic
of X is probably the last place in the world you'd want to live.
Thanks to <NAME> for reading drafts of this; <NAME> (who is 
also writing the production Arc interpreter) for several good ideas about
filtering and for creating our mail infrastructure; <NAME>,
<NAME> and <NAME> for many discussions about spam; Raph 
Levien for advice about trust metrics;  and <NAME> 
and <NAME> for advice about statistics.

You'll find this essay and 14 others in
Hackers & Painters.


More Info:Plan for Spam FAQBetter Bayesian FilteringFilters that Fight BackWill Filters Kill Spam?Japanese TranslationSpanish TranslationChinese TranslationProbabilitySpam is DifferentFilters vs. BlacklistsTrust MetricsFiltering ResearchMicrosoft PatentSlashdot ArticleThe Wrong WayLWN: Filter ComparisonCRM114 gets 99.87%
