25 citations · 53 across the 10 of their papers we have counts for
11 papers
Nearly sharp comparison results for sliced and max-sliced Wasserstein distances
Jonathan Niles-Weed, Jacob Shkrob
We prove new comparison results between the Wasserstein distance and its sliced and max-sliced counterparts. First, we show that the Hölder exponent~ obtained by Bob…
Delocalization of bias in unadjusted Hamiltonian Monte Carlo and underdamped Langevin
Yifan Chen, Xiaoou Cheng, Jonathan Niles-Weed +1
Unadjusted samplers such as unadjusted Hamiltonian Monte Carlo and underdamped Langevin are well-known to be biased. Metropolis--Hastings adjustment has been conventionally incorpo…
Convergence of Unadjusted Langevin in High Dimensions: Delocalization of Bias
Yifan Chen, Xiaoou Cheng, Jonathan Niles-Weed +1
The unadjusted Langevin algorithm is commonly used to sample probability distributions in extremely high-dimensional settings. However, existing analyses of the algorithm for stron…
Central Limit Theorems for Smooth Optimal Transport Maps
Tudor Manole, Sivaraman Balakrishnan, Jonathan Niles-Weed +1
One of the central objects in the theory of optimal transport is the Brenier map: the unique monotone transformation which pushes forward an absolutely continuous probability law o…
Distributional Convergence of the Sliced Wasserstein Process
Jiaqi Xi, Jonathan Niles-Weed
Motivated by the statistical and computational challenges of computing Wasserstein distances in high-dimensional contexts, machine learning researchers have defined modified Wasser…
Plugin Estimation of Smooth Optimal Transport Maps
Tudor Manole, Sivaraman Balakrishnan, Jonathan Niles-Weed +1
We analyze a number of natural estimators for the optimal transport map between two distributions and show that they are minimax optimal. We adopt the plugin approach: our estimato…
Sharp Convergence Rates for Empirical Optimal Transport with Smooth Costs
Tudor Manole, Jonathan Niles-Weed
We revisit the question of characterizing the convergence rate of plug-in estimators of optimal transport costs. It is well known that an empirical measure comprising independent s…
Estimation of Wasserstein distances in the Spiked Transport Model
Jonathan Niles-Weed, Philippe Rigollet
We propose a new statistical model, the spiked transport model, which formalizes the assumption that two probability distributions differ only on a low-dimensional subspace. We stu…
Convergence of Smoothed Empirical Measures with Applications to Entropy Estimation
Ziv Goldfeld, Kristjan Greenewald, Yury Polyanskiy +1
This paper studies convergence of empirical measures smoothed by a Gaussian kernel. Specifically, consider approximating , for $\mathcal{N}_σ\triangleq\mathcal{…
Minimax estimation of smooth densities in Wasserstein distance
Jonathan Niles-Weed, Quentin Berthet
We study nonparametric density estimation problems where error is measured in the Wasserstein distance, a metric on probability distributions popular in many areas of statistics an…
Optimal rates of estimation for multi-reference alignment
Afonso S. Bandeira, Philippe Rigollet, Jonathan Weed
In this paper, we establish optimal rates of adaptive estimation of a vector in the multi-reference alignment model, a problem with important applications in fields such as signal…