Hidden Markov Model
A model of sequences generated by hidden states that transition over time and emit observable outputs.
Definition
A hidden Markov model (HMM) describes a system that moves among unobserved states following Markov transition probabilities, with each state emitting observable outputs. The observer sees the emissions and infers the hidden state sequence.
The Markov assumption, that the next state depends only on the current one, is what makes the algorithms efficient, but it also limits the model when real dependencies reach further back. Higher-order and hierarchical variants relax this at the cost of more parameters.
Though largely superseded by neural sequence models for large-scale tasks, HMMs remain valuable where interpretability and small data matter, since their discrete states often correspond to meaningful regimes. Their training can converge to poor local optima, so multiple initializations are common. They also introduce the dynamic-programming ideas, forward-backward and Viterbi, that recur across sequence modeling.
Core algorithms
- Forward-backward: probability of the observations.
- Viterbi: most likely hidden state sequence.
- Baum-Welch: learn parameters from data.
Why it matters
HMMs were foundational for speech recognition, part-of-speech tagging, and bioinformatics. They remain valuable where a system has interpretable discrete states and modest data, and they introduce the sequence-modeling ideas that recurrent networks later generalized.
Fusion connection
State-based sequence models can label phases of a simulated plasma discharge, such as ramp-up, flat-top, and termination, from diagnostic time series.