106 Figure 1. The MEGA model proposed in [DauméIII and Marcu, 2006]. This model assumes the **data** is in fact generated by three distributions, a target, a common and and source. The MEGA model learns a classifier for each space. Left is the standard logistic regression model. der these assumptions
P t (x, y) P s (x, y) = P t (x) P s (x) P t (y|x) P s (y|x) (8) = P t (x) P s (x) .(9)
Again, a well founded solution can be identified by appropriate instance weighting of the loss function. [Shimodaira, 2000] explored this approach and show that the weighted model better estimate the **data** given a biased sampling function. The quantity Pt(x) Ps(x) can be estimated using e.g. nonparametric kernel estimation [Sugiyama andMülcer, 2005, Shimodaira, 2000]. [Huang et al., 2007] proposed to directly estimate the ratio, i.e. the difference between the two distributions. They use the Kernel Mean Match,
1 N s N s i=1 β i φ(x s i ) − 1 N t N t i=1 φ(x t i ) 2 ,(10)
metric that measures the distribution distance in a Reproducing Kernel Hilbert Space.