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I'm trying to predict events that are represented by a vector of 70 values. They are continues values ranging from 0 to 1. I'm fitting a model that outputs 70 numbers for every sample. Normally for classification one would pick the highest value as the prediction, but I'm going to keep all of them as I'm trying to use all of these value. Is this something reasonable to do? Any public available information available for this?

For example, I could try to predict someone's preference about topics in school. My Y would look something like this:

[1 0.5 0.9 0]
  • 1 being the most preferred topic say statistics
  • 0.5 being the neutral topic computer science
  • 0.9 being the second most preferred topic say economics
  • 0 being the least preferred topic say history

and I will have features in X for every sample to fit a ANN model to these numbers, at the end instead of picking one highest number, I'm going to keep all values and the values would look something like this

[0.9 0.4 0.7 0.2]

Is there anything related to what I'm trying to do? Looking for sources for additional information.

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  • $\begingroup$ It seems to me your Y is really only ordinal in nature. My guess is that would be very difficult for a standard ANN to learn (although there may be specialized ANNs developed for that). $\endgroup$
    – gung - Reinstate Monica
    Commented Dec 2, 2015 at 19:58

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Caveat: I'm going for an answer, but it might just be a large comment.

In a situation like softmax (predicting multiple classes) probabilities are spread out over several classes/ output variables. The class with the highest probability is usually chosen. The reason that all the classes are put together in a single model is that the probabilities should sum to one. This is a constraint on the outcomes.

In your case, there is no maximum 'mass' of preference as in softmax; i.e. there is no constraint that says that a student can not have more than 25 preference points over say 70 classes. This means that there is no reason to estimate all the preferences in a single model.

Estimating 70 different models would be normal practice.

HTH

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  • $\begingroup$ What if I rescale [1 0.5 0.9 0] by diving the sum to [0.42 0.21 0.37 0]. Then my predictions would be the probabilities that my sample's preference for each topic. Since they are from range 0-1 and also sum to one, then the output makes sense? $\endgroup$
    – Aiden Zhao
    Commented Dec 4, 2015 at 18:34
  • $\begingroup$ Yes you could also scale the vector to length one, see: chortle.ccsu.edu/vectorlessons/vch06/vch06_10.html $\endgroup$
    – spdrnl
    Commented Dec 5, 2015 at 19:17
  • $\begingroup$ @YongkangZhao That's known as the softmax. $\endgroup$
    – Wayne
    Commented Jun 5, 2019 at 13:25

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