Hidden Markov Models by Hand: States & Emissions, the Forward Algorithm, Viterbi Decoding, Smoothing & Simple Learning from Counts
Uncover hidden states from what you can observe. You will set up transition and emission tables, compute sequence probabilities with the forward algorithm, find the most likely hidden path with Viterbi and backtracking, smooth with forward–backward, estimate tables from labelled counts and tag a short toy sentence, with every cell checked as you go.
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About this course
This course builds a hidden Markov model one table at a time on a toy ferry logbook, where the weather is hidden and only the ferry status is recorded. You complete a transition table and push a distribution forward, then multiply start, transition and emission probabilities for all eight weather paths behind three days. The forward algorithm adds those paths efficiently, Viterbi finds the best one with MAX and back-pointers. You compare paths with log-probabilities, fill backward tables for posterior probabilities, estimate the tables from labelled counts with add-one smoothing and finally tag a short original sentence with three word classes.
Lessons
- Markov Chains Refresher: Transition Tables, Rows That Sum to 1 and Two-Step Probabilities Pro
- Hidden States & Emissions: The Joint Probability of a Weather Path and a Logbook Pro
- The Forward Algorithm: α Tables Step by Step and the Probability of a Logbook Pro
- Viterbi Decoding: δ Tables with MAX, Back-Pointers and the Best Path by Backtracking Pro
- Log Probabilities: Underflow, LN Sums Instead of Products and Comparing Paths Pro
- Backward & Smoothing: β Tables and the Posterior Probability of Each Day's Weather Pro
- Learning from Counts: Transition and Emission Tables from a Labelled Logbook, with Add-One Smoothing Pro
- Toy Part-of-Speech Tagging: Three Hidden Tags, Viterbi on a Short Sentence, Accuracy and a Posterior Chart Pro