Chinese restaurant process
E1031255
The Chinese restaurant process is a stochastic process used in Bayesian nonparametrics to generate random partitions of data with an unbounded number of clusters, often serving as an intuitive metaphor for how customers (data points) choose tables (clusters).
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
Bayesian nonparametric prior
ⓘ
exchangeable partition probability model ⓘ stochastic process ⓘ |
| appliedIn |
document clustering
ⓘ
genetics and population models via Ewens sampling formula ⓘ nonparametric mixture models for density estimation ⓘ topic models such as hierarchical Dirichlet process ⓘ |
| assumes | exchangeability of data points ⓘ |
| clusterSizeDistribution | power-law-like behavior under Pitman–Yor generalization ⓘ |
| construction | sequential seating of customers at tables according to specified probabilities ⓘ |
| field |
Bayesian statistics
ⓘ
machine learning ⓘ probability theory ⓘ |
| generalizationOf | finite mixture model with unknown number of components ⓘ |
| hasMetaphor |
customers correspond to data points
ⓘ
restaurant corresponds to the partition structure ⓘ tables correspond to clusters ⓘ |
| hasParameter |
concentration parameter alpha
ⓘ
discount parameter in two-parameter variant ⓘ |
| hasVariant | two-parameter Chinese restaurant process ⓘ |
| implies | random partition structure over positive integers ⓘ |
| introducedInContext | Bayesian nonparametric modeling of partitions ⓘ |
| limitBehavior | number of occupied tables grows like O(α log n) ⓘ |
| mathematicalObject | distribution over partitions of {1,…,n} for each n ⓘ |
| probabilityFormula |
P(join table k) = n_k / (n + α)
ⓘ
P(new table) = α / (n + α) ⓘ |
| probabilityRule |
probability of joining existing table k is proportional to its current number of customers
ⓘ
probability of starting a new table is proportional to alpha ⓘ |
| property |
allows countably infinite number of clusters
ⓘ
almost surely finite number of occupied clusters for finite data ⓘ exchangeable with respect to customer order ⓘ reinforcement property ⓘ rich-get-richer behavior ⓘ |
| relatedTo |
Chinese restaurant franchise
ⓘ
Dirichlet process NERFINISHED ⓘ Dirichlet process mixture model NERFINISHED ⓘ Ewens sampling formula NERFINISHED ⓘ Indian buffet process NERFINISHED ⓘ Pitman–Yor process NERFINISHED ⓘ Poisson–Dirichlet distribution NERFINISHED ⓘ stick-breaking construction of the Dirichlet process ⓘ |
| symbolForConcentrationParameter | α ⓘ |
| usedFor |
Bayesian nonparametric clustering
ⓘ
constructing Dirichlet process mixture models ⓘ defining priors over partitions ⓘ generating random partitions of data ⓘ latent feature discovery in data ⓘ modeling an unbounded number of clusters ⓘ topic modeling ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.