Some papers (e.g., {1}) claim that Baum–Welch is the same as forward–backward algorithm, but I agree with Masterfool and Wikipedia: Baum–Welch is an expectation-maximization algorithm that uses the forward–backward algorithm. The two illustrations also distinguish Baum–Welch from the forward–backward algorithm.

It is the scores/probabilities in the dynamic programming arrays that are different. As you point out these values are used in the Baum-Welch re-estimation procedure. They are also used when calculating posterior probabilities. If all you require is the single full probability value you will only need the forward (or backward) algorithm.

Oct 18, 2020 · Both the forward algorithm and the forward-backward algorithm are expected to provide a probability for the hidden states. For a live estimate of the state, does it pay to add latency to the output and to use the forward-backward algorithm rather than the forward algorithm? How to quantify the estimation improvement?

Nov 14, 2018 · The forward-backward algorithm. This presentation of the forward-backward algorithm is similar to the textbook treatment found in Greenberg (2013) Introduction to Bayesian Econometrics (pp. 193-195).

Dec 14, 2021 · Stepwise feature selection is a "greedy" algorithm for finding a subset of features that optimizes some arbitrary criterion. Forward, backward, or bidirectional selection are just variants of the same idea to add/remove just one feature per step that changes the criterion most (thus "greedy").

The forward algorithm would do this for you. If you get a relatively high likelihood, there's a good chance that $\lambda$ produced $\mathbf{X}$. If you had two HMMs $\lambda_1$ and $\lambda_2$, you might conclude the one with the higher likelihood is the best model to explain your $\mathbf{X}$.

Mar 28, 2019 · The HMM parameters are estimated using a forward-backward algorithm also called the Baum-Welch algorithm. The Viterbi algorithm is used to get the most likely states sequnce for a given observation sequence. Therefore, the two algorithms you mentioned are used to solve different problems. Classically there are 3 problems for HMMs:

Dec 1, 2018 · In short, the Forward-Backward algorithm uses the conditional independence assumptions of HMMs to compute marginals efficiently by picking an order for summing out random variables. It is a special case of the Sum-Product algorithm , which does the same thing for graphical models more generally.

Morat's answer is false on one point: Baum-Welch is an Expectation-Maximization algorithm, used to train an HMM's parameters. It uses the forward-backward algorithm during each iteration. The forward-backward algorithm really is just a combination of the forward and backward algorithms: one forward pass, one backward pass.

May 26, 2012 · The forward-backward algorithm requires a transition matrix and prior emission probabilities. It is not clear where they were specified in your case because you do not say anything about the tools you used (like the package that contains the function posterior ) and earlier events of your R session.