In probability theory, the Chinese restaurant process is a discrete-time stochastic process, whose value at any positive-integer time n is a partition Bn of the set {1, 2, 3, ..., n} whose probability distribution is determined as follows. At time n = 1, the trivial partition { {1} } is obtained with probability 1. At time n + 1 the element n + 1 is either:
- added to one of the blocks of the partition Bn, where each block is chosen with probability |b|/(n + 1) where |b| is the size of the block, or
- added to the partition Bn as a new singleton block, with probability 1/(n + 1).
The random partition so generated is exchangeable in the sense that relabeling {1, ..., n} does not change the distribution of the partition, and it is consistent in the sense that the law of the partition of n − 1 obtained by removing the element n from the random partition at time n is the same as the law of the random partition at time n − 1.
Read more about Chinese Restaurant Process: Definition, Generalization, Applications
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