1

I have a poll with four answers (A,B,C,D) and response information about people who have taken that poll. I have created four models (one for each of the answers) in a one vs all. i.e. the model for answer A has answer A as a 1 and the rest of the responses as a 0, for the second model answer B is 1 and the rest are 0, and so on...

My question is if I predict a new response given a new responser's information, are all the probabilities guaranteed to equal 1? Written as:

$$P(A|X) + P(B|X) + P(C|X) + P(D|X) \stackrel{?}{=} 1$$

It should be noted that each of the models might have different levels of regularization. I have convinced myself that if all the models have full regularization or no regularization this will hold true. But I'm not sure in the general case (one test case I have does but I don't know if it's dumb luck)

sedavidw
  • 610
  • Why not use a multinomial logit, which explicitly allows for more than two responses? Then probabilities are guaranteed to sum to one. – Nameless Oct 20 '14 at 23:42
  • That would be ideal (and might be the end result) but the system I've inherited currently creates models this way and it would require significant work to change it. This way isn't a problem for classification (which is why I suspect it was originally built this way) but now we have need for explicit probabilities and I've stumbled upon this problem – sedavidw Oct 21 '14 at 13:38
  • I am not entirely sure if it always adds up to 1. But even if it doesnt, just renormalize: $P(A|X)/[P(A|X)+P(B|X)+P(C|X)+P(D|X)]$. – Nameless Oct 21 '14 at 21:41
  • @Nameless that was something I considered but I couldn't find a good theoretical justification for it. But the practicality of it seems sound for me. If you write that up as an answer you'll get the check. Thanks – sedavidw Oct 23 '14 at 13:32
  • 1
    Let's wait and see if somebody else has an actual answer, and not just a quick and dirty trick. ;) – Nameless Oct 23 '14 at 23:13

0 Answers0