Exchangeable Trait Allocations

Understand

Trait allocations are a class of combinatorial structures in which data may belong to multiple groups and may have different levels of belonging in each group.

• Often the data are also exchangeable, i.e., their joint distribution is invariant to reordering.
• In clustering---a special case of trait allocation---exchangeability implies the existence of both a de Finetti representation and an exchangeable partition probability function (EPPF), distributional representations useful for computational and theoretical purposes.
• In this work, we develop the analogous de Finetti representation and exchangeable trait probability function (ETPF) for trait allocations, along with a characterization of all trait allocations with an ETPF.