  Mixtures of regression are a powerful class of models for regression learning
with respect to a highly uncertain and heterogeneous response variable of
interest. In addition to being a rich predictive model for the response given
some covariates, the parameters in this model class provide useful information
about the heterogeneity in the data population, which is represented by the
conditional distributions for the response given the covariates associated with
a number of distinct but latent subpopulations. In this paper, we investigate
conditions of strong identifiability, rates of convergence for conditional
density and parameter estimation, and the Bayesian posterior contraction
behavior arising in finite mixture of regression models, under exact-fitted and
over-fitted settings and when the number of components is unknown. This theory
is applicable to common choices of link functions and families of conditional
distributions employed by practitioners. We provide simulation studies and data
illustrations, which shed some light on the parameter learning behavior found
in several popular regression mixture models reported in the literature.
