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Also known as: HMM
A probabilistic sequence model with hidden states that emit observable symbols, assuming Markovian transitions between states.
DESCRIPTION
A Hidden Markov Model represents sequences via latent states that evolve as a Markov chain while emitting observations. Inference tasks include decoding the most likely state sequence (Viterbi) and learning parameters (Baum–Welch/EM). HMMs are used in speech recognition, POS tagging, bioinformatics, and time-series segmentation. They are generative and interpretable but assume conditional independence that may be unrealistic. Modern deep models often outperform HMMs on complex data, yet HMMs remain valuable for structured, interpretable sequence modeling.
ALTERNATIVE DEFINITIONS
Wikipedia
A hidden Markov model (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process with unobserved (i.e., hidden) states.
Emphasizes Markov process assumption and unobserved states.
MathWorks
A hidden Markov model is a statistical model that assumes the system being modeled is a Markov process with unobservable states.
Vendor documentation focused on statistical assumptions and tooling context.
RELATED TERMS
Markov Chain Viterbi Algorithm Baum–Welch Algorithm Dynamic Bayesian Network State Space Model Kalman Filter Sequence Modeling Part-of-Speech Tagging Speech Recognition
COMPETING TERMS
Conditional Random Field Recurrent Neural Network
RELATIONS
- Broader: Model
KNOWLEDGE AREAS
TARGET AUDIENCE
Data Scientist AI Engineer MLOps Engineer
EXTERNAL SOURCES
- Wikipedia - Hidden Markov model
- MathWorks - Overview and functions for HMMs
- hmmlearn - Python library for HMMs
- pomegranate - HMM API and examples
TOP QUESTIONS
What problem does a Hidden Markov Model solve well?
HMMs excel at modeling sequences with latent structure, such as speech phonemes or biological states, where the process is assumed Markovian and emissions are conditionally independent given the state.
Category: Usage
How is inference performed in a Hidden Markov Model?
Common procedures include Viterbi decoding for the most likely state path and forward–backward algorithms for marginal posteriors. Baum–Welch (EM) estimates parameters from data.
Category: Technique
What are the main assumptions behind HMMs?
The next state depends only on the current state (Markov property), and observations are conditionally independent given the current hidden state.
Category: Assumptions
How do HMMs compare to Conditional Random Fields?
HMMs are generative, modeling joint distributions, while CRFs are discriminative, modeling p(labels|observations). CRFs often yield better predictive performance when features are rich.
Category: Comparison
When might an HMM underperform modern deep models?
On complex, high-dimensional data with long-range dependencies, RNNs or Transformers typically outperform HMMs. HMMs still win on small data and when interpretability matters.
Category: Opinion
How many states should a Hidden Markov Model have?
Choose based on domain understanding, information criteria (AIC/BIC), or cross-validation. Overly many states can overfit; too few miss structure.
Category: Requirements
What is a common mistake when training HMMs?
Initializing parameters poorly and not using multiple random starts can trap EM in bad local optima. Regularization and priors can help.
Category: Mistakes
How do you handle continuous emissions in HMMs?
Use Gaussian or mixture-of-Gaussian emissions, or nonparametric alternatives. Fit via EM and ensure covariance regularization for stability.
Category: Technique
What is a practical application of HMMs in industry?
In predictive maintenance, HMMs model machine health states from sensor data to detect degradation and schedule interventions.
Category: Example