Gaussian processes are used in many machine learning applications that rely on
uncertainty quantification. Recently, computational tools for working with these models in …

We investigate statistical properties of a likelihood approach to nonparametric estimation of
a singular distribution using deep generative models. More specifically, a deep generative …

Bayesian clustering typically relies on mixture models, with each component interpreted as a
different cluster. After defining a prior for the component parameters and weights, Markov …

We show that deep neural networks achieve dimension-independent rates of convergence
for learning structured densities such as those arising in image, audio, video, and text …

We consider the problem of estimating a structured multivariate density, subject to Markov
conditions implied by an undirected graph. In the worst case, without Markovian …

We consider noisy observations of a distribution with unknown support. In the deconvolution
model, it has been proved recently [19] that, under very mild assumptions, it is possible to …

Manifold learning obtains a low-dimensional representation of an underlying Riemannian
manifold supporting high-dimensional data. Kernel density estimates of the low-dimensional …

Given iid sample from a stratified mixture of immersed manifolds of different dimensions, we
study the minimax estimation of the underlying stratified structure. We provide a constructive …

Non-Euclidean spaces routinely arise in modern statistical applications such as in medical
imaging, robotics, and computer vision, to name a few. While traditional Bayesian …

In high-dimensional statistics, the manifold hypothesis presumes that the data lie near low-
dimensional structures, called manifolds. This assumption helps explain why machine …