Top comment is srean, which I will shamelessly copy here:
This is more of tweak of naive Bayes than Bayes’ theorem and I suspect he is being a bit tongue in cheek and not letting on whats behind the tweak.
I am sure you have heard that naive Bayes makes gratuitous assumptions of independence. What is not mentioned as often is that it also assumes the document has been generated by a memory-less process.
So if I were to generate a document according to the model assumed by naive Bayes, and I want to decide if I should concatenate another “the” in the document, then I dont need to keep track of how many “the”s that I have already added to the document. As a result the probability of multiple occurrence n_i of a word i goes down exponentially, like this
P(n_i) = p_i^n_i.
Many words do not behave like this. Their probability do not go down monotonically from the start, rather, for words like “the” their probabilities (conditioned on their history) climb initially and then go down.
Naive Bayes works surprisingly well in spite of their grossly violated assumptions. There are many explanations for that. However, we usually forget that to make NB work, we have to throw away “stop-words”. Among them are those exact “memory-full” words that violate NB’s assumptions.
where c is a constant for that word id i. For English, c usually lies in the ball park of −1.5 to −2.1
The tweak that Norvig mentions is not an exact match for power law assumptions but it comes very close. Its using a power law assumption but with sub-optimal parameters. In fact using the power law assumption and with their parameters estimated from the data you could get an even better classifier. Though be careful of the industry of seeing power laws everywhere. Log normal distributions can look deceptively similar to a power law and is more appropriate on many such occasions.
Yeah Naive Bayes has a bad assumption of independence, but there is no reason that they have to be memory-less too and that is partly what the tweak fixes, and the theorem isn’t really being violated.
Yep. It’s hard or impossible to know in advance what will catch fire, so the safest thing is to just post things to LW, Hacker News, and a relevant subreddit. I’m usually too lazy to.
I should have posted it over at Hacker News and get +103 karma instead of −1 :-)
You could have got positive karma here too if you didn’t present it incorrectly as a challenge to:
If it ever turns out that Bayes fails—receives systematically lower rewards on some problem, relative to a superior alternative, in virtue of its mere decisions—then Bayes has to go out the window.
-- Eliezer Yudkowsky, Newcomb’s Problem and Regret of Rationality
You could have got positive karma here too if you didn’t present it incorrectly as a challenge to...
As a “challenge to”? I incorrectly assumed that it is a good example in support of something Eliezer said, namely that you choose the winning way and not your favorite heuristic.
As a “challenge to”? I incorrectly assumed that it is a good example in support of something Eliezer said, namely that you choose the winning way and not your favorite heuristic.
I suppose it would actually be a support of Eliezer’s ‘choose the winning way’ theme while simultaneously undermining everything he said about probability theory.
Either way, it is the incorrect framing not just the location that dampened reception here.
Hacker News discussion: http://news.ycombinator.com/item?id=3693447
Top comment is srean, which I will shamelessly copy here:
I should have posted it over at Hacker News and get +103 karma instead of −1 :-)
Yep. It’s hard or impossible to know in advance what will catch fire, so the safest thing is to just post things to LW, Hacker News, and a relevant subreddit. I’m usually too lazy to.
You could have got positive karma here too if you didn’t present it incorrectly as a challenge to:
As a “challenge to”? I incorrectly assumed that it is a good example in support of something Eliezer said, namely that you choose the winning way and not your favorite heuristic.
I suppose it would actually be a support of Eliezer’s ‘choose the winning way’ theme while simultaneously undermining everything he said about probability theory.
Either way, it is the incorrect framing not just the location that dampened reception here.