A basic assumption of something as simple as OLS regression is that the covariates are continuous. Often this is only partly the case, e.g. heart rate is often reported in integer number of bpm, yet the underlying value is clearly continuous, not discrete.
When doing kernel density estimation, there are suggestions for how to deal with this, e.g. the kernelheaping package in R. (which seems to rely on an explicit model for how rounding is done in things like questionnaires)
I'm wondering if there are ways of formally handling the effects of rounding in regression scenarios, and also in general for arbitrary (supervised) learning algorithms? In particular, for the heart rate example, I intuitively think that rounding doesn't matter too much, if I have enough data...can this intuition be formalised? e.g. "if the average rounding amount is so and so small compared to
<some measure of spread of the data set>, then don't worry"? At what point does the rounding become so severe that I should treat the data as categorical?