Semi-supervised learning (SSL) has tremendous value in practice due to the utilization of
both labeled and unlabelled data. An essential class of SSL methods, referred to as graph …

Plugin estimation of smooth optimal transport maps Page 1 The Annals of Statistics 2024, Vol.
52, No. 3, 966–998 https://doi.org/10.1214/24-AOS2379 © Institute of Mathematical Statistics …

This study analyses the main challenges, trends, technological approaches, and artificial
intelligence methods developed by new researchers and professionals in the field of …

In this paper we improve the spectral convergence rates for graph-based approximations of
weighted Laplace-Beltrami operators constructed from random data. We utilize regularity of …

We investigate a family of regression problems in a semisupervised setting. The task is to
assign real-valued labels to a set of n sample points provided a small training subset of N …

The performance of traditional graph Laplacian methods for semi-supervised learning
degrades substantially as the ratio of labeled to unlabeled data decreases, due to a …

In this paper we study Lipschitz regularity of elliptic PDEs on geometric graphs, constructed
from random data points. The data points are sampled from a distribution supported on a …

Neural networks have been very successful in many applications; we often, however, lack a
theoretical understanding of what the neural networks are actually learning. This problem …

We investigate graph-based Laplacian semi-supervised learning at low labeling rates (ratios
of labeled to total number of data points) and establish a threshold for the learning to be well …

In nonparametric regression, it is common for the inputs to fall in a restricted subset of
Euclidean space. Typical kernel-based methods that do not take into account the intrinsic …