Comment on the paper “On the memory complexity of the forward–backward algorithm,” by Khreich W., Granger E., Miri A., Sabourin, R.

• The EFFBS algorithm, proposed by Khreich et. al (2010) as an alternative to the Baum-Welch recursions, is reviewed.
• The EFFBS algorithm suffers from a numerical problem that limits its applicability in estimating HM models.
• The problem is due to an accumulation of a round-off error that leads the solution to diverge form the correct one.
• A possible explanation of the reasons of the error is given together with some illustrative examples.

We illustrate the Efficient Forward Filtering Backward Smoothing (EFFBS) algorithm proposed by Khreich et al. (2010) for estimation of hidden Markov models. The algorithm is aimed at reducing the amount of memory required by the Baum-Welch recursions, while having the same complexity in terms of number of operations. In implementing the EFFBS algorithm we found a numerical problem that limits its applicability. We discuss this problem in detail, providing some possible explanations of the causes of the error, together with two illustrative examples.