Log In Sign Up

Local Exchangeability

by   Trevor Campbell, et al.

Exchangeability---in which the distribution of an infinite sequence is invariant to reorderings of its elements---implies the existence of a simple conditional independence structure that may be leveraged in the design of probabilistic models and efficient inference algorithms. In practice, however, this assumption is too strong an idealization; the distribution typically fails to be exactly invariant to permutations and de Finetti's representation theory does not apply. Thus there is the need for a distributional assumption that is both weak enough to hold in practice, and strong enough to guarantee a useful underlying representation. We introduce a relaxed notion of local exchangeability---where swapping data associated with nearby covariates causes a bounded change in the distribution. Next, we prove that locally exchangeable processes correspond to independent observations from an underlying measure-valued stochastic process, showing that de Finetti's theorem is robust to perturbation and providing further justification for the Bayesian modelling approach. We also provide an investigation of approximate sufficiency and sample continuity properties of locally exchangeable processes on the real line. The paper concludes with examples of popular statistical models that exhibit local exchangeability.


page 1

page 2

page 3

page 4


Approximate Implication with d-Separation

The graphical structure of Probabilistic Graphical Models (PGMs) encodes...

Tractability through Exchangeability: A New Perspective on Efficient Probabilistic Inference

Exchangeability is a central notion in statistics and probability theory...

Contextual Weak Independence in Bayesian Networks

It is well-known that the notion of (strong) conditional independence (C...

Effective grading refinement for locally linearly independent LR B-splines

We present a new refinement strategy for locally refined B-splines which...

On Existence Theorems for Conditional Inferential Models

The framework of Inferential Models (IMs) has recently been developed in...

Yurinskii's Coupling for Martingales

Yurinskii's coupling is a popular tool for finite-sample distributional ...