Hidden Markov Models
In this section, we will give a brief outline of what an HMM is. The mathematics behind HMMs is extensive and beyond what we can cover here. Instead, we will focus on describing what they are and how they work conceptually.
An HMM is a first-order discrete Markov process. This means it has a set of states between which it transitions, governed by a transition matrix. The difference from the first-order discrete Markov processes of the previous sections is that we don’t directly observe those states. The states are hidden from us. They are latent, hence the term hidden in an HMM.
What we observe is a sequence of symbols that are emitted at each point along the state sequence. Why is this useful? One of the main benefits is that we can model situations where we think there are distinctly different phases or modes of behavior that we want to understand, but we can’t directly observe those different modes. Instead, we can only observe the symbols...
