Decision making in Markov chains applied to the problem of pattern recognition
IEEE Transactions on Information Theory
Bayes Smoothing Algorithms for Segmentation of Binary Images Modeled by Markov Random Fields
IEEE Transactions on Pattern Analysis and Machine Intelligence
Non-stationary fuzzy Markov chain
Pattern Recognition Letters
Fuzzy pairwise Markov chain to segment correlated noisy data
Signal Processing
Extension of higher-order HMC modeling with application to image segmentation
Digital Signal Processing
Hidden hybrid Markov/semi-Markov chains
Computational Statistics & Data Analysis
On the memory complexity of the forward-backward algorithm
Pattern Recognition Letters
Unsupervised segmentation of hidden semi-Markov non-stationary chains
Signal Processing
Estimation, learning, and adaptation: systems that improve with use
SSPR'12/SPR'12 Proceedings of the 2012 Joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
Joint source and sending rate modeling in adaptive video streaming
Image Communication
A modified hidden Markov model
Automatica (Journal of IFAC)
| Hi-index | 0.10 |
In this note, we examine the forward-backward algorithm from the computational viewpoint of the underflow problem inherent in Baum's (1972) original formulation. We demonstrate that the conversion of Baum's computation of joint likelihoods into the computation of posterior probabilities results in essentially the same algorithm, except for the presence of a scaling factor suggested by Levinson et al. (1983) on rather heuristic grounds. The resulting algorithm is immune to the underflow problem, and Levinson's scaling method is given a theoretical justification. We also investigate the relationship between Baum's algorithm and the recent algorithms of Askar and Derin (1981) and Devijver (1984).