Chinese Restaurant Process

From GM-RKB
(Redirected from Chinese restaurant process)
Jump to navigation Jump to search

A Chinese Restaurant Process is a discrete-time stochastic process whose value at any positive-integer time [math]\displaystyle{ n }[/math] is a partition [math]\displaystyle{ B_n }[/math] of the set [math]\displaystyle{ \{1, 2, 3, ..., n\} }[/math] 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:

  1. 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
  2. added to the partition Bn as a new singleton block, with probability 1/(n + 1).


References

2014

  • (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/Chinese_restaurant_process Retrieved:2014-5-14.
    • 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:
      1. 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
      2. 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.

2008

  • (Ahmed & Xing, 2008) ⇒ A. Ahmed and Eric Xing. (2008). “Dynamic Non-parametric Mixture Models and the Recurrent Chinese Restaurant Process: With Applications to Evolutionary Clustering.” In: Proceedings of SDM.

2006