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Usually, in machine learning textbooks the $X$ dataset and the target $y$ are defined with exact values.

How about the case if the values of both $X$ and $y$ have noises: for instance, we only know that $0.5 <= x_1 <= 0.63$ but not the precise value. How could I integrate the information into the model?

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  • $\begingroup$ If you consider Linear Regression to be machine learning (which I think you should), then you can check out Errors-in-Variables Models $\endgroup$ – klumbard Nov 5 '18 at 19:31
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There is a vast literature on this topic, you may want to have a look at this paper, for example

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