Question Regarding Multi-label probability predictions

Question

I have been doing a problem in which I have to predict probabilities for each of the labels in a multi-label (four to be precise) classification problem.

Example of a solution:

Id, North,          East,            West,           South
1,  0.71663940211,  0.037567315693,  0.03525987339,  0.0021068944991
...

The training data is of the form where each y(i) is labelled either 0,1,2 or 3 (encoded for N,E,W & S respectively)

I will be grateful if you can just tell me how to approach this problem. Links giving direct insight to the problem will also sufficient.

Answer 1

A question is a bit broaden as you do not specify if you do not know how to do it in theory or how to tackle it with a ML method.

Some of ML methods:

LogisticRegression in sklearn handles multiple class

lr = LogisticRegression()
lr.fit(X, y)
class_probabilities = lr.predict_proba(X)  # outputs the probabilities

You might also want to consider Support Vector Machines.

Theory:

You can do a "one vs rest" when you train a single classifier per class taking the sample of all other classes as negative example. (see wiki article for that)