Assume there is a data set {(x_i, y_i)}, 0<=i<n, there exist some samples that have the same x value but different y values (x_i == x_j && y_i != y_j) because there is noise when collecting data.

A common method maybe grouping them with a single y, like their mean value.

But are there any researches resolving this kind of data without grouping them together?

If yes, what is this kind of problems called? Or some keywords for doing search.

Thank you in advance!