  The goal of this paper is to introduce a general argumentation framework for
regression in the errors-in-variables regime, allowing for full flexibility
about the dimensionality of the data, error probability density types, the
(linear or nonlinear) model type and the avoidance of ad-hoc definitions of
loss functions. In this framework we introduce model fitting for partially
unpaired data, i.e. for given data groups the pairing information of input and
output is lost (semi-supervised). This is achieved by constructing mixture
model densities, which directly model this loss of pairing information allowing
for inference. In a numerical simulation study linear and nonlinear model fits
are illustrated as well as a real data study is presented based on life
expectancy data from the world bank utilizing a multiple linear regression
model. These results allow the conclusion that high quality model fitting is
possible with partially unpaired data, which opens the possibility for new
applications with unfortunate or deliberate loss of pairing information in the
data.
