Infinite Hidden Markov Model

The Infinite Hidden Markov model (also known as HDP-HMM) has a potentially infinite number of latent states:

(define vocabulary '(chef omelet soup eat work bake))

(define (get-state) (DPmem 0.5 gensym))

(define state->transition-model 
  (mem 
    (lambda (state) 
      (DPmem 1.0 (get-state)))))

(define (transition state) 
  (sample (state->transition-model state)))

(define state->observation-model 
  (mem 
    (lambda (state) 
      (dirichlet (make-list (length vocabulary) 1)))))

(define (observation state) 
  (multinomial vocabulary (state->observation-model state)))

(define (sample-words last-state) 
  (if (flip 0.2) 
      '() 
      (pair (observation last-state) 
            (sample-words (transition last-state)))))

(sample-words 'start)

(define vocabulary '(chef omelet soup eat work bake))

(define (get-state) 
  (DPmem 0.5 gensym))

(define state->transition-model 
  (mem 
    (lambda (state) 
      (DPmem 1.0 (get-state)))))

(define (transition state)
  (if (flip .2)
      'stop
      (state->transition-model state)))

(define state->observation-model 
  (mem 
    (lambda (state) 
      (dirichlet (make-list (length vocabulary) 1)))))

(define (observation state) 
  (multinomial vocabulary (state->observation-model state)))

(define (unfold p f g seed)
  (if (p seed)
      '()
      (pair (f seed)
            (unfold p f g (g seed)))))

(define (stop? state)
  (eq? state 'stop))
   
(define (sample-ihmm)
  (unfold stop? observation transition 'S))

(sample-ihmm)