Feature Shift

Unlike joint distribution shift detection, which cannot localize which features caused the shift, we define a new hypothesis test for each feature individually. Naïvely, the simplest test would be to check if the marginal distributions have changed for each feature (as explored by [25]); however, the marginal distribution would be easy for an adversary to simulate (e.g., by looping the sensor values from a previous day). Thus, marginal tests are not sufficient for our purpose. Therefore, we propose to use conditional distribution tests. More formally, our null and alternative hypothesis for the j-th feature is that its full conditional distribution (i.e., its distribution given all other features) has not shifted for all values of the other features.