  We present a novel approach for learning an HMM whose outputs are distributed
according to a parametric family. This is done by {\em decoupling} the learning
task into two steps: first estimating the output parameters, and then
estimating the hidden states transition probabilities. The first step is
accomplished by fitting a mixture model to the output stationary distribution.
Given the parameters of this mixture model, the second step is formulated as
the solution of an easily solvable convex quadratic program. We provide an
error analysis for the estimated transition probabilities and show they are
robust to small perturbations in the estimates of the mixture parameters.
Finally, we support our analysis with some encouraging empirical results.
