Hidden Markov Models › Visualizing HMM Structure

Michael BrenndoerferUpdated May 7, 20252 min read
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Chapter 40Hidden Markov Models › Visualizing HMM Structure
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The transition matrix is the heart of an HMM's syntactic knowledge. By visualizing it as a heatmap, we can see which tag sequences the model considers likely and which it considers rare. This provides insight into both the structure of English grammar and the quality of our learned model. Notice that the matrix is quite sparse: most entries are small because most tag pairs rarely occur consecutively in well-formed English. The few high-probability entries correspond to the syntactic rules that generate most English sentences.

Out[19]:
Visualization
Heatmap showing transition probabilities between POS tags with color intensity indicating probability values.
Transition probability matrix learned from the Brown corpus. Darker cells indicate higher probabilities. Clear patterns emerge: determiners strongly predict nouns, nouns often precede verbs, and punctuation frequently follows nouns and verbs. These transitions encode the statistical regularities of English syntax.

The transition matrix reveals clear syntactic patterns. Determiners (DET) have high transition probability to nouns (NOUN) and adjectives (ADJ). Nouns frequently transition to verbs (VERB) or punctuation. Prepositions (ADP) strongly predict nouns. This reflects prepositional phrase structure. These patterns are exactly what we'd expect from English grammar.