Hidden Markov Models

Hidden Markov Models (HMMs) are statistical models that are used to model time series data, where the underlying process is assumed to be a Markov process with hidden states. HMMs are widely used in speech recognition, natural language processing, bioinformatics, and many other fields. The basic idea behind HMMs is to model the observed data as a sequence of observations that are generated by an underlying Markov process with hidden states. The hidden states are not directly observable, but can be inferred from the observed data using the Baum-Welch algorithm or other similar algorithms. HMMs are characterized by a set of parameters, including the initial state distribution, the transition probabilities between states, and the emission probabilities of the observations given the states. These parameters can be learned from data using the Expectation-Maximization (EM) algorithm or other similar algorithms.
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