A data augmentation approach for a class of statistical inference problems

We present an algorithm for a class of statistical inference problems. The main idea is to
reformulate the inference problem as an optimization procedure, based on the generation of
surrogate (auxiliary) functions. This approach is motivated by the MM algorithm, combined
with the systematic and iterative structure of the Expectation-Maximization algorithm. The
resulting algorithm can deal with hidden variables in Maximum Likelihood and Maximum
a Posteriori estimation problems, Instrumental Variables, Regularized Optimization and
Constrained Optimization problems. The advantage of the proposed algorithm is to provide
a systematic procedure to build surrogate functions for a class of problems where hidden
variables are usually involved. Numerical examples show the benefits of the proposed
approach.