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CrossCat is a generative model that can be used for categorizing objects given their features. The model assumes that each data point is generated using multiple systems of categories; each such system accounts for some subset of the features.

(define samples

  (mh-query 300 100
   (define kind-distribution (DPmem 1.0 gensym))
   (define feature->kind
     (mem (lambda (feature) (kind-distribution))))
   (define kind->class-distribution
     (mem (lambda (kind) (DPmem 1.0 gensym))))
   (define feature-kind/object->class
     (mem (lambda (kind object) ((kind->class-distribution kind)))))
   (define class->parameters
     (mem (lambda (object-class) (beta 1 1))))
   (define (observe object feature)
     (flip (class->parameters 
             (feature-kind/object->class (feature->kind feature) 
   (list (observe 'spinach 'breakfast)
         (observe 'eggs 'breakfast))
   (and (observe 'eggs 'breakfast)
        (observe 'toast 'breakfast)
        (observe 'eggs 'dinner)
        (observe 'spinach 'dinner))))

(hist samples)