Finite forms of de Finetti's theorem on exchangeability

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Subjective Probability: The Real Thing (2004, unknown): “We have worked with a somewhat different notion in Diaconis and Freedman (1978c) and developed a theory general enough to include a wide variety of statistical models.”
Probabilistic Symmetries and Invariant Neural Networks (2020, background): “The de Finetti conditional i.i.d. representation (1) may fail for a finitely exchangeable sequence (see Diaconis, 1977; Diaconis and Freedman, 1980a, for examples).”
Less is Different: Emergence and Reduction Reconciled (2011, background): “In the classical case, this means that a permutation-invariant probability measure is a unique mixture, not of product measures, but of hypergeometric measures (cf. Diaconis 1977, Diaconis and Freedman 1980, Jeffrey 1988, pp. 240-245).”
Janossy Pooling: Learning Deep Permutation-Invariant Functions for Variable-Size Inputs (2018, methodology): “Some researchers may be more familiar with the concept of inﬁnite exchange-ability through de Finetti’s theorem (De Finetti, 1937; Diaconis, 1977), which imposes strong structural requirements: the probability of any subsequence must equal the marginalized probability of the original sequence…”