  In many applications (e.g., medical studies), the population of interest
(e.g., disease status) comprises heterogeneous subpopulations. The mixture of
probabilistic regression models is one of the most common techniques to
incorporate the information of covariates into learning of the population
heterogeneity. Despite its flexibility, the model may lead to unreliable
estimates in the presence of multicollinearity problem. In this paper, we
develop Liu-type shrinkage methods through an unsupervised learning approach to
estimate the model coefficients in multicollinearity. The performance of the
developed methods is evaluated via classification and stochastic versions of EM
algorithms. The numerical studies show that the proposed methods outperform
their Ridge and maximum likelihood counterparts. Finally, the developed methods
are applied to analyze the bone mineral data of women aged 50 and older.
