The Infinite Relational Model (IRM) is a nonparametric model that, given data involving different kinds of entities, discovers which kinds there are and which relations hold between kinds. From the paper by Ref:Kemp2006uv:
“Suppose we are given one or more relations involving one or more types. The goal of the IRM is to partition each type into clusters, where a good set of partitions allows relationships between entities to be predicted by their cluster assignments. For example, we may have a single type people and a single relation likes(i,j) which indicates whether person i likes person j. Our goal is to organize the entities into clusters that relate to each other in predictable ways (Figure 1a).”
(define samples
(mh-query
300 100
(define class-distribution (DPmem 1.0 gensym))
(define object->class
(mem (lambda (object) (class-distribution))))
(define classes->parameters
(mem (lambda (class1 class2) (beta 0.5 0.5))))
(define (talks object1 object2 conditioning-value)
(flip (classes->parameters (object->class object1)
(object->class object2))
conditioning-value))
(list (equal? (object->class 'tom) (object->class 'fred))
(equal? (object->class 'tom) (object->class 'mary)))
(and (talks 'tom 'fred true)
(talks 'tom 'jim true)
(talks 'jim 'fred true)
(not (talks 'mary 'fred false))
(not (talks 'mary 'jim false))
(not (talks 'sue 'fred false))
(not (talks 'sue 'tom false))
(not (talks 'ann 'jim false))
(not (talks 'ann 'tom false))
(talks 'mary 'sue true)
(talks 'mary 'ann true)
(talks 'ann 'sue true)
)))
(hist (map first samples) "tom and fred in same group?")
(hist (map second samples) "tom and mary in same group?")
References: