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05/23/2023
Towards Understanding the Dynamics of Gaussian-Stein Variational Gradient Descent
Stein Variational Gradient Descent (SVGD) is a nonparametric particle-ba...
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04/03/2023
High-dimensional scaling limits and fluctuations of online least-squares SGD with smooth covariance
We derive high-dimensional scaling limits and fluctuations for the onlin...
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02/20/2023
High-dimensional Central Limit Theorems for Linear Functionals of Online Least-Squares SGD
Stochastic gradient descent (SGD) has emerged as the quintessential meth...
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05/24/2022
Randomly Initialized One-Layer Neural Networks Make Data Linearly Separable
Recently, neural networks have been shown to perform exceptionally well ...
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07/04/2021
Rates of Estimation of Optimal Transport Maps using Plug-in Estimators via Barycentric Projections
Optimal transport maps between two probability distributions μ and ν on ...
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10/05/2020
Measuring Association on Topological Spaces Using Kernels and Geometric Graphs
In this paper we propose and study a class of simple, nonparametric, yet...
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05/14/2019
Multivariate Ranks and Quantiles using Optimal Transportation and Applications to Goodness-of-fit Testing
In this paper we study multivariate ranks and quantiles, defined using t...
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01/19/2018