Let's say we have a binary classification task, but our dataset contains more fine grained values of how much an examples belongs to the class or not. So the labels are real numbers in $\left[0,1\right]$. I can see two ways to make use of this additional information:

  • Approach this as a classification problem and use the cross entropy loss, but just have non-binary labels. This would basically mean, we interpret the soft labels are a confidence in the label that the model might pick up during learning.

  • Frame this as a regression problem, where we want to predict the exact amount of how much an example belongs to the class. In this case, we would use a regression loss like MSE or Huber loss.

What is the difference between the two approaches? How do I decide between them?

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    $\begingroup$ This isn't part of the question, but you could use a logistic regression, which makes use of both the target and the proportions. $\endgroup$ – Firebug Aug 27 '16 at 0:59
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    $\begingroup$ One approach is to use quasi-likelihood, where you would essentially just be doing ordinary logistic regression only on a continuous response. To fit this model you would use quasi or quasibinomial as the family argument in R's glm function. $\endgroup$ – dsaxton Aug 27 '16 at 2:18
  • $\begingroup$ @dainjar so what's been your best working shot at it so far? how did the cross-entropy approach work for your case? $\endgroup$ – matt Mar 17 '18 at 11:34

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