Concentration bounds for sums of exchangeable random variables under arbitrary marginals

Determine whether concentration inequalities can be obtained for sums of exchangeable random variables under an arbitrary marginal distribution, relying only on exchangeability and without further structural assumptions on the marginal.

Background

The paper studies concentration inequalities when independence is relaxed to exchangeability, a symmetry assumption common in statistics and machine learning. Variance-free bounds like Hoeffding’s inequality are central to generalization guarantees but typically require i.i.d. assumptions.

The authors explicitly pose whether such concentration bounds can be obtained for sums of exchangeable random variables under arbitrary marginals and then proceed to provide affirmative results via de Finetti’s representation, yielding Hoeffding-type bounds relative to extrema of means in the support of the mixing measure.