BaumWelchalgoritmen

The Baum-Welch algorithm is a dynamic programming algorithm used for training Hidden Markov Models (HMMs). It is an expectation-maximization (EM) algorithm that iteratively refines the parameters of an HMM to maximize the probability of observing a given sequence of data. The algorithm was developed by Leonard E. Baum and his colleagues.

The core idea of the Baum-Welch algorithm is to estimate the hidden state sequence given the observed data, and then use this estimated sequence to update the HMM parameters. It proceeds in two main steps: the expectation (E-step) and the maximization (M-step). In the E-step, the algorithm computes the expected number of times each transition and emission occurs, given the current model parameters and the observed sequence. This is typically done using the forward and backward algorithms. In the M-step, the algorithm re-estimates the HMM parameters (transition probabilities and emission probabilities) based on these expected counts to maximize the likelihood of the observed data.

The algorithm is guaranteed to converge to a local maximum of the likelihood function. It is widely used in various applications, including speech recognition, natural language processing, bioinformatics, and financial modeling, where it helps to model sequential data with underlying unobserved states. The algorithm requires an initial set of HMM parameters, and the quality of the learned model can depend on this initialization.