A rough guide to the Aldous-Hoover representation theorem for exchangeable arrays

Abstraction: Representation theorem for row-and-column exchangeable random arrays

Key points:

• A sequence is exchangeable if its distribution is permutation-invariant; de Finetti's theorem shows such sequences are conditionally i.i.d. given a latent variable alpha
• David Aldous (1981) extended this to 2D arrays X_ij invariant under row and column permutations (jointly exchangeable / RCE arrays)
• The Aldous-Hoover theorem: any RCE array can be written as X_ij = f(alpha, xi_i, eta_j, lambda_ij) for i.i.d. uniform random variables and a measurable function f
• Applications include modelling networks, graphs, and collaborative filtering where row/column ordering is arbitrary
• Talk by Dr Daniel Roy at Cambridge CBL, May 2012, part of the Machine Learning Reading Group series

Connections: Daniel Roy · Exchangeability · De Finetti Theorem · Random Arrays

Source: http://talks.cam.ac.uk/talk/index/37509