Why can't I detect concept drift with linear regression? When I was first trying to detect concept drift, it seemed naively to me to be a problem of detecting whether noisy data was veering off horizontal trajectory (non-trivial slope above some arbitrary threshold that I'd consider a statistically significant slope).
I have a deployed model that's been predicting for months. I sampled data from each month, and then split those samples into segments, and in each segment kept track of a label's frequency in that dataset proportional to the size of it - the amount of times the label was predicted in the segment divided by the overall number of datapoints in the segment. I end up with noisy data $L$, and I'd imagine if drift were to occur that $L$ would have some sufficiently non-trivial slope.
There are lots of fancy methods I could use to detect drift using skmultiflow like ADWIN, but the first thing that came to mind was simple linear regression. Why can't I just fit a line to  the noisy data and see if its slope is not constant? Or, what if I used tsmoothie to smooth the noisy data and fit a line on that? Am I oversimplifying things, and that's why methods like ADWIN exist?
Say, for instance, I used tsmoothie and ended up with the following smoothed signal:

What's stopping me from taking a linear regression of that dark blue line?

There are two troubling aspects to that.

*

*Just because you get an insignificant regression slope doesn’t mean a lack of drift. It could just mean a lack of ability to detect the drift due to lacking power in the hypothesis test. These are different. If you are able to declare an effect size of interest (so a slope that would make you take notice and wonder what is happening), however, then techniques like equivalence testing and TOST can be valuable.


*Depending on what kind of drift there is, linear regression might not be able to detect it. For instance, linear regression will totally miss a sinusoidal pattern where you drift and then return, drift and then return, drift and then return. If that sounds okay, that’s just one of infinitely many possibilities that a linear regression will miss. (Yes, linear regression can use nonlinear basis functions to model sinusoidal patterns. However, you have to tell then regression to use that basis function, and that requires you to determine, ahead of time, what you want to detect.)
