Hidden Markov Models
A hidden Markov model (HMM) is a statistical model of the temporal evolution of a process. The model is based on the assumption that the future can be predicted from current state, since it summarizes the past sequence of events. In order to model the temporal dynamics of a system, each state has a certain probability of transitioning to every other state; the true state path is hidden in the HMM. The observations of information from the
HMM are stochastically related to the state, but the state itself is never observed directly (Rabiner 1989). In the case of music alignment, only the acoustic features of the signal can be observed, and it is not known whether a given frame is from either an attack state or a sustain state. In their earliest applications for music alignment, single-level HMMs were used, but they proved to be unreliable at times. More recent works have explored the use of multilevel and graphical models.
Today we are going to go over two examples from my own work.
Improving MIDI-audio alignment with acoustic features
Estimating Onset and Offset Asynchronies in Polyphonic Score-Audio Alignment
More reading on machine learning
Rabiner’s tutorial on HMMs
Michael Jordan’s (unfinished) book on graphical models
Trevor Hastie, Robert Tibshirani, and Jerome Friedman’s Elements of Statistical Learning
Christopher Bishop’s Pattern Recognition and Machine Learning