A Robust Scaling Approach for Implementation of HsMMs

The underflow problem of the forward-backward algorithm is a crucial issue for implementation of Hidden semi-Markov models (HsMM). A widely used solution is to scale up the forward and backward variables at each time step. We demonstrate the conventional scaling approach is not robust with several examples, then propose an improved scaling approach which is warranted to be robust and applicable to all HsMM variants. With the proposed method, all the variables are proved to be properly scaled up at the expense of acceptable computational complexity. Numerical experiments validate these claims.