Hidden Markov Model
IntermediateProbabilistic model for sequential data with latent states.
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Why It Matters
Hidden Markov Models are important for analyzing sequential data in various fields, including speech recognition, finance, and genetics. Their ability to model time-dependent processes makes them a valuable tool for predicting future states based on past observations.
A Hidden Markov Model (HMM) is a statistical model that represents systems with hidden states and observable outputs. It is characterized by a Markov process where the system transitions between hidden states according to a set of probabilities, and each hidden state emits observable outputs according to a probability distribution. Formally, an HMM is defined by the parameters: the state transition probabilities, the emission probabilities, and the initial state distribution. The model is typically trained using the Baum-Welch algorithm, a form of the Expectation-Maximization algorithm, and inference is performed using the Viterbi algorithm or the Forward-Backward algorithm. HMMs are widely used in applications such as speech recognition, bioinformatics, and time series analysis, and are foundational in the study of sequential data modeling.