9 papers
Nonparametric Riemannian Empirical Bayes, and Denoising Measurements on Manifolds
Adam Quinn Jaffe, Leonardo V. Santoro, Bodhisattva Sen
We initiate the study of nonparametric empirical Bayes denoising methods in the setting where both the latent variables and their measurements lie on a compact Riemannian manifold,…
Fréchet Means in Infinite Dimensions
Adam Quinn Jaffe
While there exists a well-developed asymptotic theory of Fréchet means of random variables taking values in a general "finite-dimensional" metric space, there are only a few known…
Wasserstein-Cramér-Rao Theory of Unbiased Estimation
Nicolás GarcÃa Trillos, Adam Quinn Jaffe, Bodhisattva Sen
The quantity of interest in the classical Cramér-Rao theory of unbiased estimation (e.g., the Cramér-Rao lower bound, its exact attainment for exponential families, and asymptoti…
Coupling Theory, Optimal Transport, and Strassen's Theorem for Eventual Domination
Adam Quinn Jaffe, Daniel Raban
Many results in probability (most famously, Strassen's theorem on stochastic domination), characterize some relationship between probability distributions in terms of the existence…
Consistency and inconsistency in -means clustering
Moïse Blanchard, Moïse Blanchard, Adam Quinn Jaffe +1
A celebrated result of Pollard proves asymptotic consistency for -means clustering when the population distribution has finite variance. In this work, we point out that the popu…
A Strong Duality Principle for Equivalence Couplings and Total Variation
Adam Quinn Jaffe
We introduce and study a notion of duality for two classes of optimization problems commonly occurring in probability theory. That is, on an abstract measurable space $(Ω,\mathcal…