  Transfer learning research attempts to make model induction transferable
across different domains. This method assumes that specific information
regarding to which domain each instance belongs is known. This paper helps to
extend the capability of transfer learning for linear regression problems to
situations where the domain information is uncertain or unknown; in fact, the
framework can be extended to classification problems. For normal datasets, we
assume that some latent domain information is available for transfer learning.
The instances in each domain can be inferred by different parameters. We obtain
this domain information from the distribution of the regression coefficients
corresponding to the explanatory variable $x$ as well as the response variable
$y$ based on a Dirichlet process, which is more reasonable. As a result, we
transfer not only variable $x$ as usual but also variable $y$, which is
challenging since the testing data have no response value. Previous work mainly
overcomes the problem via pseudo-labelling based on transductive learning,
which introduces serious bias. We provide a novel framework for analysing the
problem and considering this general situation: the joint distribution of
variable $x$ and variable $y$. Furthermore, our method controls the bias well
compared with previous work. We perform linear regression on the new feature
space that consists of different latent domains and the target domain, which is
from the testing data. The experimental results show that the proposed model
performs well on real datasets.
