Hidden Markov Model
IntermediateEnglish: Hidden Markov Model
Probabilistic model for sequential data with latent states.
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.
Definition
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.