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Hidden Markov models – short Q&A
20 questions and answers on hidden Markov models, explaining states, transitions, emissions, decoding and training for sequence labeling tasks.
What is a Hidden Markov Model (HMM)?
Answer: An HMM is a probabilistic model for sequences with hidden states that evolve according to a Markov chain and emit observed symbols according to state-specific emission distributions.
What components define an HMM?
Answer: An HMM is defined by a set of hidden states, an initial state distribution, a transition probability matrix between states and an emission probability distribution from states to observations.
How is an HMM used for POS tagging?
Answer: In POS tagging, tags are treated as hidden states and words as emissions; the model learns transition probabilities between tags and emission probabilities of words given tags to label new sentences.
What is the Markov property in an HMM?
Answer: The Markov property assumes that the next hidden state depends only on the current state, not on the full history of states, making transitions governed by a first-order Markov chain.
What is the Viterbi algorithm used for in HMMs?
Answer: The Viterbi algorithm efficiently finds the single most likely sequence of hidden states (the best path) given an observed sequence, using dynamic programming over states and time steps.
What is the forward algorithm in HMMs?
Answer: The forward algorithm computes the probability of the observation sequence by summing over all possible state paths recursively, enabling efficient evaluation of sequence likelihood under the model.
What is the backward algorithm and when is it used?
Answer: The backward algorithm computes probabilities of future observations given a state at time t; together with forward probabilities it is used in training procedures like Baum–Welch for parameter estimation.
What is the Baum–Welch algorithm?
Answer: Baum–Welch is an expectation-maximization algorithm for training HMM parameters from unlabeled sequences, iteratively computing expected counts of transitions and emissions and re-estimating probabilities.
How do transition probabilities differ from emission probabilities?
Answer: Transition probabilities govern how likely the model is to move from one hidden state to another, while emission probabilities specify how likely each observed symbol is given the current hidden state.
What is the difference between decoding and training in HMMs?
Answer: Decoding (e.g. with Viterbi) infers the most likely hidden state sequence given fixed parameters, while training estimates those parameters (transitions and emissions) from data using labeled or unlabeled sequences.
How can we train an HMM in a supervised way?
Answer: With labeled state sequences, we can estimate transition and emission probabilities using relative frequencies from the annotated data, often with smoothing to handle unseen events.
What is the role of smoothing in HMM parameter estimation?
Answer: Smoothing prevents zero probabilities for unseen transitions or emissions, ensuring the model can still assign non-zero probability to new sequences at inference time, similar to n-gram smoothing.
How does an HMM differ from a simple Markov chain?
Answer: A Markov chain models observable states directly, while an HMM introduces hidden states that generate observable outputs, allowing modeling of latent structure behind observed sequences.
Why are HMMs considered generative models?
Answer: HMMs model the joint distribution over hidden states and observations, specifying how sequences are generated; they can be sampled to produce synthetic observation sequences consistent with the learned parameters.
What is state posterior decoding in HMMs?
Answer: Posterior decoding chooses at each time step the state with the highest posterior probability given the entire observation sequence, which can differ from the single best global path found by Viterbi.
How do HMMs handle variable-length sequences?
Answer: HMMs naturally handle sequences of different lengths because probabilities are defined over transitions between states for each time step; algorithms like Viterbi and forward-backward iterate over sequence length.
What are some limitations of HMMs for NLP tasks?
Answer: HMMs rely on strong independence assumptions, have limited ability to incorporate rich overlapping features and can struggle with long-range dependencies compared to CRFs or neural sequence models.
Where are HMMs still used in modern NLP or speech?
Answer: Although often replaced by neural models, HMMs are still used in some speech recognition systems, low-resource tagging setups and as interpretable baselines or teaching tools.
How can we visualize an HMM?
Answer: HMMs are often visualized as state diagrams where nodes represent hidden states and directed edges labeled with probabilities represent transitions, with additional arrows to emitted observation symbols.
How do HMM ideas influence more advanced sequence models?
Answer: Concepts like hidden states, transition structure and dynamic programming for inference inspire modern architectures and algorithms, including CRFs and certain probabilistic or hybrid neural sequence models.
🔠HMM concepts covered
This page covers hidden Markov models: structure, forward-backward and Viterbi algorithms, supervised and unsupervised training and their role in classical NLP sequence tagging.