Regression / Predictive Methods for Arbitrary Input and Output with Intervals

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Does anybody know any regression/prediction/supervised learning method if I have arbitrary independent and dependent variables with Intervals?

For example, I have an observation with epistemic uncertainty that modeled as interval such as:

x_1 x_2 y
[1,3] [3,4] [-1,0]
[-2,0] [1,4] [4,5.5]
[2,3] [6,8] [5,8]
... ... ...

How can I model this kind of data with regression technique?

I found some solutions mentioned interval censored data. But I guess, that's not the case. I also found some others, but they seem to only allow the uncertainty propagation from the independent variable to the dependent variables. Meanwhile, in my case, I think I need to include the interval dependent variable into the fitting/training process.

Does anybody knows any reference for this problem?