On learning parametric-output HMMs
This provides a method for learning parametric-output HMMs, which is incremental as it builds on existing HMM frameworks with a decoupled approach.
The authors tackled the problem of learning Hidden Markov Models (HMMs) with parametric outputs by decoupling the task into estimating output parameters via a mixture model and then solving a convex quadratic program for transition probabilities, achieving robust error bounds and encouraging empirical results.
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.