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Statistical Speech Processing
Published in Shaila Dinkar Apte, Random Signal Processing, 2017
The backward algorithm calculates recursively backward variables going backward along the observation sequence. The forward algorithm is typically used for evaluating the probability of an observation sequence to be emitted by an HMM. Both algorithms are used for finding the optimal state sequence and estimating the HMM parameters. The recursion can be described as
A Revealing Introduction to Hidden Markov Models
Published in Mark Stamp, Introduction to Machine Learning with Applications in Information Security, 2017
The forward algorithm only requires about NT multiplications. This is in stark contrast to the naïve approach, which has a work factor of more than 2 TNT. Since T is typically large and N is relatively small, the forward algorithm is highly efficient.
A Machine Learning Approach for Quantifying the Design Error Propagation in Safety Critical Software System
Published in IETE Journal of Research, 2022
HMM is a well-proven formalism [18] to estimate the hidden or unknown parameters in a model. We believe that HMM model certainly helps to detect certain patterns to make predictions and it is descriptive to gain knowledge from data. In HMM, the states are not observable, but when a state is visited, an observation is recorded that is a probabilistic function of the state. There is no correspondence between hidden states and observable state. In HMM, there are three problems, the answers of which are required to be found. These are finding the actual probability for an observation sequence, finding the state sequence having highest derivation probability for this observation sequence when an observation sequence is given, and obtaining the model parameters through data set when a training (learning) data set is given. Forward algorithm is used for solving the problem given in the first case, Viterbi algorithm is used for solving the problem in the second case, and Forward–Backward algorithm is used for solving the problem in the last state along with Expectation Maximization or Baum-Welch algorithm. The framework for forecasting failure is shown in Figure 7.