Assumptions of stationarity does limit things a bit, but it might be possible to extend the argument to weak or limited dependence. Once I was looking at this p

Assumptions of stationarity does limit things a bit, but it might be possible to extend the argument to weak or limited dependence. Once I was looking at this problem with some differential geometry lenses. Adapting to your setting, the nearest neighbors would be computed according to a data dependent metric not just Euclidean. The working hypothesis was that under normal circumstances the process is constrained to be in the vicinity of some lower dimensional manifold. This is reasonable because of the many "near invariants" among the dimensions. Wonder why no one really bites this. I think the only way to monetize this would be to build one's own where monitoring is done better, and not sell better monitoring to others. Unfortunately that's a very capital intensive option. Someday we should chat more on this.