F-measure versus Accuracy

I had a bit of a revelation a few years ago. In retrospect, it's obvious. And I'm hoping someone else out there hasn't realized this because otherwise I'll feel like an idiot. The realization was that F-measure (for a binary classification problem) is not invariant under label switching. That is, if you just change which class it is that you call "positive" and which it is that you call "negative", then your overall F-measure will change.

What this means is that you have to be careful, when using F-measure, about how you choose which class is the "positive" class.

On the other hand, the simple "accuracy" metric is (of course) invariant under label switching. So when using accuracy, you needn't worry about which class you consider "positive."

In the olden days, when people pretty much just used F-measure to analyze things like retrieval quality, this wasn't a problem. It was "clear" which class was positive (good documents) and which was negative. (Or maybe it wasn't...) But now, when people use F-measure to compare results on a large variety of tasks, it makes sense to ask: when is accuracy the appropriate measure and when is F the appropriate measure?

I think that, if you were to press anyone on an immediate answer to this question, they would say that they favor F when one of the classes is rare. That is, if one class occurs only in 1% of the instances, then a classifier that always reports "the other class" will get 99% accuracy, but terrible F.

I'm going to try to convince you that while rarity is a reasonable heuristic, there seems to be something deeper going on.

Suppose I had a bunch of images of people drinking soda (from a can) and your job was to classify if they were drinking Coke or Pepsi. I think it would be hard to argue that F is a better measure here than accuracy: how would I choose which one is "positive." Now, suppose the task were to distinguish between Coke and Diet Dr. Pepper. Coke is clearly going to be the majority class here (by a long shot), but I still feel that F is just the wrong measure. Accuracy still seems to make more sense. Now, suppose the task were to distinguish between Coke and "anything else." All of a sudden, F is much more appealing, even though Coke probably isn't much of a minority (maybe 30%).

What seems to be important here is the notion of X versus not-X, rather than X versus Y. In other words, the question seems to be: does the "not-X" space make sense?

Let's consider named entity recognition (NER). Despite the general suggestion that F is a bad metric for NER, I would argue that it makes more sense than accuracy. Why? Because it just doesn't make sense to try to specify what "not a name" is. For instance, consider the string "Bill Clinton used to be the president; now it's Bush." Clearly "Bill Clinton" is a person. But is "Clinton used"? Not really. What about "
Bill the"? Or "Bill Bush"? I think a substantial part of the problem here is not that names are rare, but that it's just not reasonable to develop an algorithm that finds all not-names. They're just not well defined.

This suggests that F is a more appropriate measure for NER than, at least, accuracy.

One might argue--and I did initially myself--that this is an artifact of the fact that names are often made up of multiple words, and so there's a segmentation issue. (The same goes for the computer vision problem of trying to draw bounding boxes around humans in images, for which, again, F seems to make more sense.)

But I think I've been convinced that this isn't actually the key issue. It seems, again, that what it boils down to is that it makes sense to ask one to find Entities, but it doesn't make sense to ask one to find non-Entities, in the same way it it doesn't make sense to ask one to find non-Cokes.

(Of course, in my heart of hearts I believe that you need to use a real--i.e., type 4--evaluation metric, but if you're stuck without this, then perhaps this yields a reasonable heuristic.)