  Mixed linear regression is a well-studied problem in parametric statistics
and machine learning. Given a set of samples, tuples of covariates and labels,
the task of mixed linear regression is to find a small list of linear
relationships that best fit the samples. Usually it is assumed that the label
is generated stochastically by randomly selecting one of two or more linear
functions, applying this chosen function to the covariates, and potentially
introducing noise to the result. In that situation, the objective is to
estimate the ground-truth linear functions up to some parameter error. The
popular expectation maximization (EM) and alternating minimization (AM)
algorithms have been previously analyzed for this.
  In this paper, we consider the more general problem of agnostic learning of
mixed linear regression from samples, without such generative models. In
particular, we show that the AM and EM algorithms, under standard conditions of
separability and good initialization, lead to agnostic learning in mixed linear
regression by converging to the population loss minimizers, for suitably
defined loss functions. In some sense, this shows the strength of AM and EM
algorithms that converges to ``optimal solutions'' even in the absence of
realizable generative models.
