Is there a supervised learning algorithm that takes tags as input, and produces a probability as output?

Let's say I want to determine the probability that I will upvote a question on SO, based only on which tags are present or absent.

Let's also imagine that I have plenty of data about past questions that I did or did not upvote.

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Is there a machine learning algorithm that could take this historical data, train on it, and then be able to predict my upvote probability for future questions? Note that it must be the probability, not just some arbitrary score.

Let's assume that there will be up-to 7 tags associated with any given question, these being drawn from a superset of tens of thousands.

My hope is that it is able to make quite sophisticated connections between tags, rather than each tag simply contributing to the end result in a "linear" way (much as words do in a Bayesian spam filter).

So for example, it might be that the word "java" increases my upvote probability, except when it is present with "database", however "database" might increase my upvote probability when present with "ruby".

Oh, and it should be computationally reasonable (training within an hour or two on millions of questions).

What approaches should I research here?

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Given that there probably aren't many tags per message, you could just create "n-gram" tags and apply naive Bayes. Regression trees would also produce an empirical probability at the leaf nodes, using +1 for upvote and 0 for no upvote. See http://www.stat.cmu.edu/~cshalizi/350-2006/lecture-10.pdf for some readable lecture notes and http://sites.google.com/site/rtranking/ for an open source implementation.

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You can try several methods (linear regression, SMV, neural networks). The input vector should consist of all possible tags, where each tag represents one dimension.

Then each record in a training set has to be transformed to the input vector according to the tags. For example let's say you have different combinations of 4 tags in your training set (php, ruby, ms, sql) and you define an unweighted input vector [php, ruby, ms, sql]. Let's say you have the following 3 records whic are transformed to weighted input vectors:

php, sql -> [1, 0, 0, 1]

ruby -> [0, 1, 0, 0]

ms, sql -> [0, 0, 1, 1]

In case you use linear regression you use the following formula

y = k * X

where y represents an answer (upvote/downvote) in your case and by inserting known values (X - weighted input vectors).

How ta calculate weights in case you use linear regression you can read here but the point is to create binary input vectors which size is equal (or larger in case you take into account some other variables) to the number of all tags and then for each record you set weights for each tag (0 if it is not included or 1 otherwise).