Covariance shift [Shimodaira, 2000], is another relaxation of DA. Here, given an observation, the class distributions are same in the source and target domains, but the marginal **data** distributions are different. P t (Y |X) = P s (Y |X), but P t (X) = P s (X). This situation arise, for example, in active learning, where the P s (X) tend to be biased to lie near the margin of the classifier. At a first glance, this situation appears not to present a problem, since P t (Y |X) = P s (Y |X), which we can estimate from the data. Here is why it becomes a problem in practice. Assuming, first of all, that the model family we use is mismatched to the data, i.e. regardless of what parameter we choose the model won't fit the underlying distribution. Under this assumption, covariate shift becomes a problem for the following reason. The optimal fit of the source **data** will be such that it minimize model error in the dense area of P s (X) (because these areas will dominate the error). Now, since P t (X) is different from P s (X), the learned model will not be optimal for the target **data** (again, since the model family is mismatched).