# Is it acceptable to use class probabilities as weights for a weighted average when the bins are numbers 1 to 5?

I have a Multi Class SVM that can predict what class some observation belongs to. There are 5 classes. They are trained for observation that scored 1 to 5.

I want the MC-SVM to predict a class for some observation. The prediction is, for example, 0.5 probability to belong to class 5 and 0.5 for class 4. I know that there's a relationship between these bins where they are scores from 1 to 5. I was wondering if it makes sense to use a weighted average of these probabilities to say that the score is a weighted sum: 5 (class) * 0.5 (prob) + 4 (class) * 0.5 (prob) = 4.5 score

Does this method make sense? Is it often done? Does it have a name?

• And what will happen if the prediction is: 0.33 for class 5, 0.33 for class 4 and 0.33 for class 1? Does score of 3.33 informative for you in this case? – German Demidov Jan 19 '16 at 11:14
• That is informative. – Phlox Midas Jan 19 '16 at 11:18
• You should note that raw SVM output isn't a probability, and needs some scaling (see Platt scaling). Also, if your data are discrete but still ordered, you could cast this as a regression problem and sidestep this altogether. As it is, you could run into problems if you get 50% class 1 and 50% class 5 - your final label would be class 3, which has a 0% chance. – Nuclear Wang Jan 19 '16 at 11:19
• You're absolutely right about regression but the results of the regressions I've run have been much worse than this methods. I wasn't aware I had to Platt scale my output. So then my approach isn't sensible at the moment? Once I scale it, those numbers are acceptable? – Phlox Midas Jan 19 '16 at 11:23