Constrained Hidden Markov Models
Sam T. Roweis · 1999
By thinking of each state in a hidden Markov model as corresponding to some spatial region of a fictitious topology space it is possible to naturally define neighbouring states as those which are connected in that space. The transition matrix can then be constrained to allow transitions only between neighbours; this means that all valid state sequences correspond to connected paths in the topology space. I show how such constrained HMMs can learn to discover underlying structure in complex sequences of high dimensional data, and apply them to the problem of recovering mouth movements from acoustics in continuous speech. 1 Latent variable models for sequence data Hidden Markov models (HMMs) can be thought of as dynamic generalizations of discrete state models for static data such as vector quantization or Gaussian mixture models. They can also be though of as discrete state versions of linear dynamical systems (Kalman filter models) which are themselves dynamic generalizations of conti...