Perturbed Kullback-Leibler Deviation Bounds for Dirichlet Processes
Probability
2025-03-24 v1
Abstract
We present new and improved non-asymptotic deviation bounds for Dirichlet processes (DPs), formulated using the Kullback-Leibler (KL) divergence, which is known for its optimal characterization of the asymptotic behavior of DPs. Our method involves incorporating a controlled perturbation within the KL bound, effectively shifting the base distribution of the DP in the upper bound. Our proofs rely on two independent approaches. In the first, we use superadditivity techniques to convert asymptotic bounds into non-asymptotic ones via Fekete's lemma. In the second, we carefully reduce the problem to the Beta distribution case. Some of our results extend similar inequalities derived for the Beta distribution, as presented in [27].
Cite
@article{arxiv.2503.17255,
title = {Perturbed Kullback-Leibler Deviation Bounds for Dirichlet Processes},
author = {Pierre Perrault},
journal= {arXiv preprint arXiv:2503.17255},
year = {2025}
}