10 citations · 24 across the 15 of their papers we have counts for
16 papers
Phylogenetic Inference and the Stickiness of Fréchet Means, via Precise Asymptotics of an Embedded Random Walk
Adam Quinn Jaffe
A well-known phenomenon in statistical analyses of populations of phylogenetic trees in the Billera-Holmes-Vogtmann space is that the topology of the Fréchet mean tree can contain…
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,…
Wasserstein-Cramér-Rao Theory of Unbiased Estimation
Nicolás García 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 asymptotic…
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, Adam Quinn Jaffe, Nikita Zhivotovskiy
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…
Constrained Denoising, Empirical Bayes, and Optimal Transport
Adam Quinn Jaffe, Nikolaos Ignatiadis, Bodhisattva Sen
In latent variables models, two important goals are denoising and deconvolution: denoising aims to estimate the latent variables, whereas deconvolution aims to estimate the distrib…
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…
Large Deviations Principle for Bures-Wasserstein Barycenters
Adam Quinn Jaffe, Leonardo V. Santoro
We prove the large deviations principle for empirical Bures-Wasserstein barycenters of independent, identically-distributed samples of covariance matrices and covariance operators.…
Constructing Maximal Germ Couplings of Brownian Motions with Drift
Sebastian Hummel, Adam Quinn Jaffe
Consider all the possible ways of coupling together two Brownian motions with the same starting position but with different drifts onto the same probability space. It is known that…
Fréchet Mean Set Estimation in the Hausdorff Metric, via Relaxation
Moise Blanchard, Adam Quinn Jaffe
This work resolves the following question in non-Euclidean statistics: Is it possible to consistently estimate the Fréchet mean set of an unknown population distribution, with resp…
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{…
A Zero-One Law for Virtual Markov Chains
Adam Quinn Jaffe
A virtual Markov chain (VMC) is a sequence of Markov chains (MCs) coupled together on the same probability space such that has state space $\{0,1,\ld…
Asymptotic Theory of Geometric and Adaptive -Means Clustering
Adam Quinn Jaffe
We revisit Pollard's classical result on consistency for -means clustering in Euclidean space, with a focus on extensions in two directions: first, to problems where the data ma…
Virtual Markov chains
Steven N. Evans, Adam Q. Jaffe
We introduce the space of virtual Markov chains (VMCs) as a projective limit of the spaces of all finite state space Markov chains (MCs), in the same way that the space of virtual…
Limit Theorems for Fréchet Mean Sets
Steven N. Evans, Adam Q. Jaffe
For , the Fréchet -mean of a probability measure on a metric space is an important notion of central tendency that generalizes the usual notions in the real l…
Vietoris-Rips Complexes of Regular Polygons
Henry Adams, Samir Chowdhury, Adam Quinn Jaffe +1
Persistent homology has emerged as a novel tool for data analysis in the past two decades. However, there are still very few shapes or even manifolds whose persistent homology barc…