Related papers: Granulometric Smoothing on Manifolds

We present a framework for learning probability distributions on topologically non-trivial manifolds, utilizing normalizing flows. Current methods focus on manifolds that are homeomorphic to Euclidean space, enforce strong structural priors…

This paper advocates a novel framework for segmenting a dataset in a Riemannian manifold $M$ into clusters lying around low-dimensional submanifolds of $M$. Important examples of $M$, for which the proposed clustering algorithm is…

In this paper, we consider a k-nearest neighbor kernel type estimator when the random variables belong in a Riemannian manifolds. We study asymptotic properties such as the consistency and the asymptotic distribution. A simulation study is…

Method of parameterizing and smoothing the unknown underling distributions using Bernstein polynomials is proposed, verified and investigated. Any distribution with bounded and smooth enough density can be approximated by the proposed…

We focus on the problem of manifold estimation: given a set of observations sampled close to some unknown submanifold $M$, one wants to recover information about the geometry of $M$. Minimax estimators which have been proposed so far all…

We consider the problem of estimating a spatially varying density function, motivated by problems that arise in large-scale radiological survey and anomaly detection. In this context, the density functions to be estimated are the background…

We study the Riemannian Langevin Algorithm for the problem of sampling from a distribution with density $\nu$ with respect to the natural measure on a manifold with metric $g$. We assume that the target density satisfies a log-Sobolev…

Research on manifold learning within a density ridge estimation framework has shown great potential in recent work for both estimation and de-noising of manifolds, building on the intuitive and well-defined notion of principal curves and…

This paper begins with a description of methods for estimating image probability density functions that reflects the observation that such data is usually constrained to lie in restricted regions of the high-dimensional image space-not…

Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…

We study the smoothed log-concave maximum likelihood estimator of a probability distribution on $\mathbb{R}^d$. This is a fully automatic nonparametric density estimator, obtained as a canonical smoothing of the log-concave maximum…

We assume that $M_0$ is a $d$-dimensional $C^{2,1}$-smooth submanifold of $R^n$. Let $K_0$ be the convex hull of $M_0,$ and $B^n_1(0)$ be the unit ball. We assume that $ M_0 \subseteq \partial K_0 \subseteq B^n_1(0).$ We also suppose that…

We introduce the Riemannian Proximal Sampler, a method for sampling from densities defined on Riemannian manifolds. The performance of this sampler critically depends on two key oracles: the Manifold Brownian Increments (MBI) oracle and the…

We develop algorithms for sampling from a probability distribution on a submanifold embedded in Rn. Applications are given to the evaluation of algorithms in 'Topological Statistics'; to goodness of fit tests in exponential families and to…

Theoretical guarantees are established for a standard estimator in a semi-parametric finite mixture model, where each component density is modeled as a product of univariate densities under a conditional independence assumption. The focus…

We consider the problem of generative modeling based on smoothing an unknown density of interest in $\mathbb{R}^d$ using factorial kernels with $M$ independent Gaussian channels with equal noise levels introduced by Saremi and Srivastava…

A stochastic algorithm is proposed, finding the set of generalized means associated to a probability measure on a compact Riemannian manifold M and a continuous cost function on the product of M by itself. Generalized means include p-means…

In this study, a density-on-density regression model is introduced, where the association between densities is elucidated via a warping function. The proposed model has the advantage of a being straightforward demonstration of how one…

The ratio between two probability density functions is an important component of various tasks, including selection bias correction, novelty detection and classification. Recently, several estimators of this ratio have been proposed. Most…

Estimating the density of states of systems with rugged free energy landscapes is a notoriously difficult task of the utmost importance in many areas of physics ranging from spin glasses to biopolymers. Density of states estimation has also…