Minimax Posterior Contraction Rates for Unconstrained Distribution Estimation on $[0,1]^d$ under Wasserstein Distance

Peter Matthew Jacobs, Lekha Patel, Anirban Bhattacharya, Debdeep Pati

Abstract: We obtain asymptotic minimax optimal posterior contraction rates for estimation of probability distributions on $[0,1]^d$ under the Wasserstein-$p$ metrics using Bayesian Histograms. To the best of our knowledge, our analysis is the first to provide minimax posterior contraction rates for every $p \geq 1$ and problem dimension $d \geq 1$. Our proof technique takes advantage of the conjugacy of the Bayesian Histogram.

Submission Length: Long submission (more than 12 pages of main content)

Assigned Action Editor: ~Alp_Kucukelbir1

Submission Number: 3500