# Incorporating noise into machine learning models?

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?

• If you consider Linear Regression to be machine learning (which I think you should), then you can check out Errors-in-Variables Models – klumbard Nov 5 '18 at 19:31