Figure 5-5. A state with high probability will win over time What we see in this figure is how a state like S1 will become less relevant over time, while a state of S3 becomes even more relevant compared to the others. The arrows are shaded to show the probability dampening. What we are attempting to do with this algorithm is traverse a set of states in the most optimal way. We do this by determining the probability that a state will happen given its emissions as well as the probability that it will transition from the previous state to the current. Then we multiply those two together to get the probability that the sequence will happen. Iterating through the entire sequence, we eventually find our optimal sequence.
The Learning Problem The learning problem is probably the simplest to actually implement. Given a sequence of states and observations, what is the most likely to happen next? We can do that purely by figuring out the next step in the Viterbi sequence. We figure out the next state by maximizing the next step given the fact there is no emission available yet. But you can figure out the most probable emission from there as well as the most probable state, and that is known as the next optimal state emission combo. If this way of solving doesn’t make sense yet, don’t worry: in the next section, we will delve further into using the Viterbi algorithm. Unfortunately, there isn’t any free and easily accessible data available for analyzing user behaviors over time given page views, but there is a similar problem we can solve by using a part-of-speech tagger built purely using a Hidden Markov Model.
Part-of-Speech Tagging with the Brown Corpus Given the phrase “the quick brown fox,” how would you tag its parts of speech? We know that English has parts of speech like determiners, adjectives, and nouns. We The Learning Problem
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