Overview and Intuitive Understanding Hidden Markov Model (HMM) is a class of probabilistic models used to model and infer system evolution processes in situations where “states are unobservable”. The core problem it solves can be summarized in one sentence: When the true state of the real world cannot be directly observed, can we still infer the most likely internal state change process of the system based solely on the observed phenomena?...

Starting with an Intuitive Problem When processing audio, speech, or other time series data, we will almost certainly encounter this problem: if two signal segments are similar in “content,” but not consistent in the speed of time progression, can we still judge that they are similar? This problem is very common in real scenarios. For example, two people sing the same melody, but one sings faster and the other slower; students may slow down due to hesitation during sight-singing, retreat and re-sing after making mistakes, or suddenly accelerate at certain positions; the same sentence is spoken by different people with different speaking speeds and different pause patterns....