Related papers: Granulometric Smoothing on Manifolds
This paper proposes a novel method for testing observability in Gaussian models using discrete density approximations (deterministic samples) of (multivariate) Gaussians. Our notion of observability is defined by the existence of the…
In this paper, we propose a density estimation algorithm called \textit{Gradient Boosting Histogram Transform} (GBHT), where we adopt the \textit{Negative Log Likelihood} as the loss function to make the boosting procedure available for the…
In state space models, smoothing refers to the task of estimating a latent stochastic process given noisy measurements related to the process. We propose an unbiased estimator of smoothing expectations. The lack-of-bias property has…
We define a general method for finding a quasi-best approximant in sup-norm to a target density belonging to a given model, based on independent samples drawn from distributions which average to the target (which does not necessarily belong…
The construction and theoretical analysis of the most popular universally consistent nonparametric density estimators hinge on one functional property: smoothness. In this paper we investigate the theoretical implications of incorporating a…
Geodesic slice sampling, introduced in Durmus et al., 2024, is a slice sampling based Markov chain Monte Carlo method for approximate sampling from distributions on Riemannian manifolds. We prove that it is uniformly ergodic for…
We propose a new estimation procedure of the conditional density for independent and identically distributed data. Our procedure aims at using the data to select a function among arbitrary (at most countable) collections of candidates. By…
Data-sensitive metrics adapt distances locally based the density of data points with the goal of aligning distances and some notion of similarity. In this paper, we give the first exact algorithm for computing a data-sensitive metric called…
Given a decision process based on the approximate probability density function returned by a data assimilation algorithm, an interaction level between the decision making level and the data assimilation level is designed to incorporate the…
The Rao-Blackwell theorem is utilized to analyze and improve the scalability of inference in large probabilistic models that exhibit symmetries. A novel marginal density estimator is introduced and shown both analytically and empirically to…
One of the popular measures of central tendency that provides better representation and interesting insights of the data compared to the other measures like mean and median is the metric mode. If the analytical form of the density function…
Let $\mathbf{x}_j = \mathbf{\theta} + \mathbf{\epsilon}_j$, $j=1,\dots,n$ be i.i.d. copies of a Gaussian random vector $\mathbf{x}\sim\mathcal{N}(\mathbf{\theta},\mathbf{\Sigma})$ with unknown mean $\mathbf{\theta} \in \mathbb{R}^d$ and…
This paper addresses the problem of detecting boundary points and estimating the sampling density of a dataset derived from a compact manifold with boundary, potentially in the presence of noise. We extend recent advances in doubly…
We introduce the Binless Multidimensional Thermodynamic Integration (BMTI) method for nonparametric, robust, and data-efficient density estimation. BMTI estimates the logarithm of the density by initially computing log-density differences…
We propose practical deep Gaussian process models on Riemannian manifolds, similar in spirit to residual neural networks. With manifold-to-manifold hidden layers and an arbitrary last layer, they can model manifold- and scalar-valued…
A common method for estimating the Hessian operator from random samples on a low-dimensional manifold involves locally fitting a quadratic polynomial. Although widely used, it is unclear if this estimator introduces bias, especially in…
In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man…
Hjort and Glad (1995) present a method for semiparametric density estimation. Relative to the ordinary kernel density estimator, this technique performs much better when a parametric vehicle distribution fits the data, and otherwise…
We study generalized density-based clustering in which sharply defined clusters such as clusters on lower-dimensional manifolds are allowed. We show that accurate clustering is possible even in high dimensions. We propose two data-based…
The purpose of this paper is to study the problem of estimating a compactly supported density of probability from noisy observations of its moments. In fact, we provide a statistical approach to the famous Hausdorff classical moment…