hidden Markov model
/ HID-un MAR-kof MOD-ul /
A hidden Markov model describes a situation where something is changing through a sequence of hidden states you can't see directly, but at each step it leaves a visible clue. Picture a friend in another room whose mood (happy, tired, grumpy) you can't observe, but you can hear whether they're humming, sighing, or silent. From the stream of sounds, you try to infer the unseen sequence of moods. The 'Markov' part is a simplifying promise: tomorrow's mood depends only on today's, not on the whole history.
The model has two moving parts. Transition rules govern how the hidden state drifts from one step to the next — how likely a happy mood is to stay happy or slide to tired. Emission rules govern how each hidden state produces its visible clue — how likely a tired mood is to make a sigh. Given a recorded sequence of clues, efficient classic algorithms can compute the probability of the whole sequence, find the single most likely path of hidden states, and learn the rules from data alone.
Why it matters: hidden Markov models were the workhorse of speech recognition for decades, and they still power gene-finding in DNA, part-of-speech tagging, and activity tracking — anywhere a hidden process unfolds in time and shows itself only through noisy signals. The honest limits flow from that Markov promise: by assuming the next state forgets all but the immediate past, the model struggles with long-range structure. Modern neural sequence models often outperform it on rich data, but the HMM remains prized for being interpretable, data-efficient, and exactly solvable.
Weather inferred from seaweed. You can't see if each day is sunny or rainy (hidden states), but a piece of seaweed hanging outside is dry, damp, or soggy (observations). Soggy seaweed makes rain likely, dry makes sun likely. Given a week of seaweed readings — dry, damp, soggy, soggy, damp — the model reconstructs the most probable sequence of hidden weather.
An HMM infers an unseen sequence (the weather) from a chain of noisy clues (the seaweed), using the Viterbi algorithm.
The Markov assumption — the next state depends only on the current one — is the model's strength and its ceiling. It makes computation exact and cheap, but it deliberately forgets long-range context, so an HMM cannot capture dependencies that span many steps the way modern attention-based models can.