# Chance to belong to each of several classes

There is a project which I band my head on for some time and I'd like to hear if anyone of you faced such a task before and how they solve it:

I'm thinking of using machine learning to show people who enroll to my college their percentage chance of finishing each faculty based on different data we have on them. Now, by success, I mean how close the machine can classify the newcomer to a student who finished. Example of an output: faculty A:75%, B:80%, C:95%.

For the sake of simplicity, let's assume we have two variables: SAT and school GPA and my training data has "faculty" variable which can be A, B or C when A is considered the hardest faculty and C the easiest. In addition, I have the variable "status" which can be either "finished" or "dropped".

Now, at first I thought it is a simple multi-classification problem and wanted to use a Decision Tree, but here is the catch: a student can have success in several faculties (for example, he can finish both B and C with 100% chance) but the tree will give 50/50 to them both, which doesn't reflect the real percentage.

Then, I thought to move to one-vs-all Logistic Regression, using the three faculties and a fourth class which contains all the dropouts. However, what bugs me here is that students succeed of fail under different circumstances, for example, a student who dropped from faculty A, the hardest, has higher SAT and GPA than a student who succeeded in C thus classifying them all together feels wrong to me.

So far, the only logical solution I came up with is to run three binary Logistic Regressions for each faculty, which will learn to classify how likely a student will belong to those who succeeded. Then, to put each of my test students through those three and get the percentages I showed in the beginning.

Have I got it right or is all I wrote here a bunch of nonsense? Have I missed any better solutions to such situation?

• I have tried to correct a couple of grammatical errors in your text, can you check that the meaning is still as you intended? If not then feel free to revert my edit. The question title is also ungrammatical but I don't want to attempt to correct it because I'm not sure what you intend - do you think you could clarify it yourself? By the way, there is no need to give thanks or add a signature at the end of a question - so that the question is briefer for future readers, we prefer that you don't. Aug 13, 2017 at 21:28