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So I basically have a $n$ classes. I have an input. My data is organised in the following way: each input has a label, this label is 2 classes. It can be twice the same class, or two different classes.

So I want to output a vector with only 0s, 1s and 2s which sum is 2. Similarly to what we would do if the label is only one class in a regular classification model. I'm just a bit confused about how we would handle the standard the prediction is the argmax because here we would have to make arbitrary rules about when to predict 2 classes and when to predict two distinct classes (like in this case [0, 0.5, 0.4, 1.1, 0, 0], it's a bit hard to determine if class 4 is predicted twice or if it's one time class 2 and one time class 4, etc ...)

Is this a thing, is there a scientific term about it? Am I not supposed to do that because it breaks something fundamental about classifiers? I'm planning on training Neural Networks, XGBoost, Random Forest, Extremely Randomized Trees and comparing the different methods (are there other methods where this would be possible? basically predicting a vector whose sum is 2).

FluidMechanics Potential Flows
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  • What is the value of $n$? If it is not too large, you can create all combinations of it, and use regular one-hot vector. For example, if you have 4 classes, consider using $2^4$ = 16 output nodes – Minh-Long Luu Mar 04 '23 at 01:38
  • Very good idea although $n$ is very large in my case, around 30, making this solution probably too computationnally expensive. – FluidMechanics Potential Flows Mar 04 '23 at 11:53
  • If computation allows, I suggest setting the baseline as the One-vs-All problem first. In your case, train $n$ models, each for a specific class. – Minh-Long Luu Mar 04 '23 at 13:44
  • @Minh-LongLuu So training $n$ models that output a vector of size 3? How do I compile the outputs, it doesn't seem as straightforward as doing an argmax .. or maybe it is easy and i'm missing it? – FluidMechanics Potential Flows Mar 04 '23 at 15:38
  • Or maybe $3n$ models, 3 because for each category i have three models (binary classification): class 0 for this or something else, class 1 for this or something else and class 2 for this or something else. But I would have the same problem of compiling the outputs .. – FluidMechanics Potential Flows Mar 04 '23 at 15:42
  • I imagine it would be 30 models with 3 outputs: one is "Is this class class `i`?", two is "is the other class also this class?", and third is "no, it is another class, different from `i`". – Minh-Long Luu Mar 04 '23 at 16:17
  • 30? What do you mean? – FluidMechanics Potential Flows Mar 04 '23 at 17:42
  • And how do you aggregate the results if for example, one model predicts this is class 2 and another one predicts this is class 1? Or I guess we would take the two maximum predictions that are coherent? But what if the maximum is class 1 and the second maximum is class 2, it's not possible because sum is 2, so we look for another one that says maximum is class 1? – FluidMechanics Potential Flows Mar 04 '23 at 17:43

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