Fascinating. But are these diagrams really showing HMMs? I thought each state in an HMM had a set of transition probabilities and another set of emission probabilities, which at each step are sampled independently. In these diagrams, the two processes are coupled. If “Even Ys” were a conventional HMM, SE would sometimes emit X and transition to SO, which would result in some even and some odd runs of Y. Are these a special variant of HMM, or some other type of state machine? And would these results apply to conventional HMMs with separate transition and emission probabilities?
Fascinating. But are these diagrams really showing HMMs? I thought each state in an HMM had a set of transition probabilities and another set of emission probabilities, which at each step are sampled independently. In these diagrams, the two processes are coupled. If “Even Ys” were a conventional HMM, SE would sometimes emit X and transition to SO, which would result in some even and some odd runs of Y. Are these a special variant of HMM, or some other type of state machine? And would these results apply to conventional HMMs with separate transition and emission probabilities?