forwardback

Forwardback refers to the forward-backward algorithm, a dynamic programming method used to compute the posterior probabilities of hidden states in sequential probabilistic models such as hidden Markov models (HMMs) and related dynamic Bayesian networks. The method relies on two passes over an observation sequence: a forward pass that aggregates information from the start up to each time step, and a backward pass that propagates information from the end back to each time step. By combining the results of these passes, the algorithm yields the smoothed probability of each state at each time given the entire sequence of observations.

In practice, the forward-backward algorithm computes, for each time and state, the probability of being in that state given all observations. These smoothed probabilities are used for inference and for learning model parameters. The learning use, Baum-Welch, treats the forward-backward results as expected sufficient statistics to re-estimate transition and emission probabilities in an expectation-maximization framework.

Applications include speech recognition, biological sequence analysis, part-of-speech tagging, and financial time-series analysis. The algorithm is valued for exact inference in HMMs, though it can be computationally intensive for large state spaces, with time complexity proportional to the product of the number of states and sequence length. In practice, scaling or log-domain implementations are used to avoid numerical underflow.

Originated in the study of HMMs in the late 1980s, the forward-backward approach remains a foundational technique in probabilistic sequence modeling. The term forwardback is sometimes used informally or in software naming as a shorthand for this approach, though most literature uses “forward-backward algorithm.”

See also: forward algorithm, backward algorithm, Baum-Welch, hidden Markov model.