Hidden Markov Models
Hidden Markov Models are probabilistic algorithms that can be employed in all those contexts where it's impossible to measure the state of a system (we can only model it as a stochastic variable with a known transition probability), but it's possible to access some data connected to it. An example can be a complex engine that is made up of a large number of parts. We can define some internal states and learn a transition probability matrix (we're going to learn how to do that), but we can only receive measures provided by specific sensors.
Let's consider a stochastic process X(t) that can assume N different states: s1, s2, …, sN with first-order Markov chain dynamics. Let's also suppose that we cannot observe the state of X(t), but we have access to another process O(t), connected to X(t), which produces observable outputs (often known as emissions). The resulting process is called a Hidden Markov Model (HMM), and a generic...