Can we use any of the various types of Deep Neural Networks for Ordinal Classification? If yes, then how? If no, then what is the limiting problem? I know that CovNets with a softmax output can be used for classification between n classes. Is there a way this can be extended/modified for ordinal classification?

Finally, I would like both class label and its ordinal output.

I think ordinal classification is part of regression (please clarify). So, I am asking for a DNN that can do both classification and regression. Is this possible?


1 Answer 1


There are a few approaches. One is to do a one in hot encoding: https://arxiv.org/pdf/0704.1028.pdf

But there should be other approaches. In classical ordinal regression, we fit cut off values st:

  • $ P(X=1) = P(Z \leq \theta_1) = F(\theta_1)$
  • $ P(X=2) = P(\theta_1 \leq Z \leq \theta_2) = F(\theta_2) - F(\theta_1)$
  • $ P(X=3) = P(Z \geq \theta_2) = 1- F(\theta_2)$

Where Z is some latent variable and F is the CDF of the latent variable. It should be possible to directly apply this approach where Z is the second to last layer (the layer before the softmax).

  • $\begingroup$ Note that you are (properly) answering with regard to probability estimation. The original question was falsely put in terms of 'classification'. $\endgroup$ Jun 9, 2019 at 13:10
  • $\begingroup$ Once you have a probability for each class, the typical approach is then to choose the most probable class. $\endgroup$ Jun 10, 2019 at 18:37
  • $\begingroup$ Please don't do that unless there is a class that has a probability above 0.95 for all observations. If probabilities are more spread out there is too much uncertainty to ignore close calls. $\endgroup$ Jun 10, 2019 at 21:26
  • $\begingroup$ @FrankHarrell Where do you get 0.95 as opposed to, say, 0.90 or 0.99? $\endgroup$
    – Dave
    Sep 17, 2022 at 0:11
  • $\begingroup$ You could say 0.99 but not so much 0.9. A probability of 0.9 means you'll be wrong 0.1 of the time if you classify it as "positive" and 0.1 may be too large. $\endgroup$ Sep 17, 2022 at 15:26

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