3.3 Change of Functional Relations

Both class imbalance and covariate shift simplify the difference between $P_s(X, Y)$ and $P_t(X, Y)$. It is still possible that $P_t(X \vert Y)$ differs from $P_s(X \vert Y)$ or $P_t(Y \vert X)$ differs from $P_s(Y \vert X)$.

Jiang and Zhai (2007a) considered the case when $P_t(Y \vert X)$ differs from $P_s(Y \vert X)$, and proposed a heuristic method to remove ``misleading'' training instances from the source domain, where $P_s(y \vert x)$ is very different from $P_t(y \vert x)$. To discover these ``misleading'' training instances, some labeled data from the target domain is needed. This method therefore is only suitable for supervised domain adaptation.