Hidden Markov Model
I. Inferring hidden states behind observed data — overview of HMM
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flowchart LR
A1["Observable sequence"] -- "Analyze hidden-state transition probabilities" --> B1["Reconstruct the hidden-state path"]
style A1 fill:#f9f9f9,stroke:#333,stroke-width:1px
style B1 fill:#e1f5fe,stroke:#01579b,stroke-width:1px
Definition: a statistical Markov model in which the system’s state cannot be observed directly, but the transitions and probabilities of the hidden state ( Hidden State ) are inferred from observable data
Characteristics: ( Markov Property ) the memoryless ( Memoryless ) assumption that the future state is determined solely by the current state ( Dual Stochastic Process ) a two-layer probability structure consisting of transitions ( Transition ) between states and the emission ( Emission ) of data ( Sequence-Specialized ) well suited to pattern recognition and sequential data processing over time, such as speech recognition and stock-price prediction
II. Detailed mechanisms and components of HMM
A. The inference mechanism of HMM
graph TD
A2["Hidden State(S)\n(Hidden)"] -- "Transition probability" --> B2["Hidden State(S+1)"]
A2 -- "Emission probability" --> C2["Observed Data(O)\n(Observable)"]
B2 -- "Emission probability" --> D2["Observed Data(O+1)"]
B. Core components and the three key algorithms
| Category | Component / Algorithm | Detailed Function and Role |
|---|---|---|
| Model Parameters | Initial / Transition / Emission | Initial state probability, state-transition probability matrix, and observation-generation probability |
| Evaluation | Forward / Backward | Computes the probability that a specific sequence occurs, given the model parameters |
| Decoding | Viterbi Algorithm | Searches for the most probable hidden-state path that could have generated the observed sequence |
| Learning | Baum-Welch(EM) | Iteratively optimizes the model’s parameters from observed data |
III. Applications and technology trends of HMM
A. Major application areas
| Field | Use Case | Detailed Content |
|---|---|---|
| NLP | POS Tagging | Automatically tags the part of speech of each word in a sentence based on context |
| Bioinformatics | Gene Prediction | Identifies protein-coding regions within a gene sequence |
| Speech Recognition | Speech-to-Text | Infers the corresponding word sequence from an input speech signal |
B. Technology trends and evolution
( Deep Learning Fusion ) hybrid models combine the statistical structure of the classic HMM with the powerful context-retention ability of RNN/LSTM networks. ( Statistical Robustness ) compared to deep learning, HMMs require less computation and offer a clearer model structure, so they remain preferred in certain data-scarce domains.