# How is exchangeability related to covariate shift?

I understand that exchangeability refers to the notion that the order of data in a sequence does not affect the joint distribution of that data. In a sense, the current data we possess is from the same kind of distribution as future data we may wish to predict (i.e., we could exchange the order and it would have the same joint distribution).

This feels heavily related to the notion of covariate shift, which I understand as the phenomenon whereby the distribution over the covariates (i.e. inputs $$X$$) changes between train and test time (expressed more mathematically in the introduction to this paper.) However, this does not make an explicit mention to sequences.

My question is therefore, how are these two notions related? I.e., is exchangeability a harsher criteria of covariate shift?

• Can you explain covariate shift? – kjetil b halvorsen Dec 31 '18 at 21:58
• I understood it as the distribution over the covariates (i.e. inputs $X$) changing between train and test time. – fiorenza2 Jan 3 at 10:21
• You can edit your question including this explication, preferably with some references and more context. It will then maybe be reopened – kjetil b halvorsen Jan 3 at 12:15