Manifold learning (ML), also known as nonlinear dimension reduction, is a set of methods to
find the low-dimensional structure of data. Dimension reduction for large, high-dimensional …

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 …

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 …

We investigate the frequentist coverage properties of (certain) Bayesian credible sets in a
general, adaptive, nonparametric framework. It is well known that the construction of …

In this paper we study the statistical properties of Laplacian smoothing, a graph-based
approach to nonparametric regression. Under standard regularity conditions, we establish …

Models with dimension more than the available sample size are now commonly used in
various applications. A sensible inference is possible using a lower-dimensional structure. In …

In this paper, we study the statistical properties of Principal Components Regression with
Laplacian Eigenmaps (PCR-LE), a method for non-parametric regression based on …

In network analysis, it is common to work with a collection of graphs that exhibit
heterogeneity. For example, neuroimaging data from patient cohorts are increasingly …

Graph-based semi-supervised regression (SSR) involves estimating the value of a function
on a weighted graph from its values (labels) on a small subset of the vertices; it can be …

This paper investigates the use of methods from partial differential equations and the
calculus of variations to study learning problems that are regularized using graph …