Right. You need the total number L and D of items each user has liked or disliked. You need the total number of liked items LT, and the total number of dislik

Right. You need the total number L and D of items each user has liked or disliked. You need the total number of liked items LT, and the total number of disliked items DT, which have the tag T. Then you just iterate through the tags and multiply the prior odds by (LT/L):(DT/D) for each tag. (To avoid zeroes, you could add 1 to all the numbers above.) This will usually give you a unrealistically extreme probability estimate at the end, but it's sometimes good at classifying positive vs. negative cases. Runtime should be linear in the number of tags. If that doesn't work - don't be too surprised if it fails! - then it's time to either find something off-the-shelf, crack a textbook or hire an expert.