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This is a very general question about machine learning. Two of the most standard problems in ML are classification and regression. E.g. if we have pictures of buildings, we can classify them as two-story vs three-story, or predict their height in meters, assuming we have proper ground truth labels.

But what if you need to answer something like: "what is the lower bound on the height of this building?" In other words, assuming all of the training data is correct, what is the absolute lowest this building can be (with 99% confidence)?

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    $\begingroup$ I think it depends on whether or not you get training samples like the picture and the information 'this building has exactly xyz floors' in contrast to the image and the information 'this building consists of approximately / at least / at most / ... xyz floors'. In the first case it should be covered by confidence intervals as stated in the answer. In the other case the area of machine learning that deals with this is called 'survival analysis' (the patient survived at least xyz years and after that he/she dropped out of the study). $\endgroup$ – Fabian Werner Feb 28 at 12:55
  • $\begingroup$ Let's say my examples are the following: [image of the building]: measured height 13.5 meters For a previously unseen building, I want my neural network to output something like this building is at least 12 meters tall with 99% confidence $\endgroup$ – Aleksei Petrenko Feb 28 at 23:33
  • $\begingroup$ So that means that you have precise training data and the way to go is as sketched in the existing answer: do a regular regression and then use confidence intervals... $\endgroup$ – Fabian Werner Mar 1 at 10:35
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Regression models are often capable of calculating standard deviations for their predictions. You could then build a confidence interval.

In simpler problems like linear regression, this problem is quite easy. But I think your question is more related to more complex machine learning algorythms such as neural networks. Well, I am pretty sure it is possible to train them for that.

With random forests, you can use what the 1st percentile of the predictions made by individual trees as your lower bound, but I think you would require a huge amount of trees for this to be reliable.

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