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4.14 Hidden Markov models

You can describe an HMM's states, transitions and emissions, run the forward algorithm, and decode a sequence with Viterbi.

Before:01. Mathematics for Machine Learning 02. Python — Basics to Advanced

A hidden Markov model models a process you cannot see through observations you can, and it powered speech recognition for decades. Three problems define the subject — evaluation, decoding, learning — and two algorithms are worth working by hand: forward, for how likely a sequence is, and Viterbi, for the most likely hidden states behind it. It closes the classical AI module and quietly sets up the sequence models to come; the recurrent networks ahead answer the same three questions with learned parameters.

Work through these

Describe the states, observations, transition and emission probabilities of a hidden Markov model
A model where the thing you care about is hidden and you see only noisy consequences of it, with probabilities for moving between hidden states and for producing each observation. This structure fits an enormous range of sequence problems.
Hidden Markov Model Overview · Reference
Name the three classic problems: evaluation, decoding and learning
Three questions are asked of these models: how likely is this observation sequence, what hidden sequence best explains it, and what probabilities fit the data. Each has its own algorithm.
Work through the forward algorithm on a short observation sequence
An algorithm that computes the likelihood of an observation sequence efficiently by reusing partial results. Working it by hand on a short sequence is what makes the reuse visible.
Decode the most likely state sequence with Viterbi
Finding the single most likely hidden sequence rather than the most likely state at each moment, which are different things. That distinction is the point of the algorithm.
Explain why speech recognition reached for hidden Markov models first
Speech is a sequence of hidden linguistic units producing noisy sound, which is exactly the structure these models describe. This is why they dominated speech recognition for decades.
Hidden Markov Model Overview · Reference

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