Related papers: Density Level Set Estimation on Manifolds with DBS…
Level set methods are widely used for image segmentation because of their capability to handle topological changes. In this paper, we propose a novel parametric level set method called Disjunctive Normal Level Set (DNLS), and apply it to…
For $x\in (0,1)$, let $\langle d_1(x),d_2(x),d_3(x),\cdots \rangle$ be the Engel series expansion of $x$. Denote by $\lambda(x)$ the exponent of convergence of the sequence $\{d_n(x)\}$, namely \begin{equation*} \lambda(x)= \inf\left\{s…
A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent)…
The Chinese Space Station Survey Telescope (CSST) aims to map the universe across an unprecedented dynamic range of stellar densities, spanning from extragalactic voids to the crowded Galactic center (e.g. a few stars and galaxies in the…
We study theoretically, for the first time, the Dirichlet kernel estimator introduced by Aitchison and Lauder (1985) for the estimation of multivariate densities supported on the $d$-dimensional simplex. The simplex is an important case as…
We construct a kernel density estimator on symmetric spaces of non-compact type and establish an upper bound for its convergence rate, analogous to the minimax rate for classical kernel density estimators on Euclidean space. Symmetric…
The Density Based Spatial Clustering of Applications with Noise (DBSCAN) is a topometric algorithm used to cluster spatial data that are affected by background noise. For the first time, we propose the use of this method for the detection…
We extend our previous results on local asymptotic normality (LAN) for qubits, to quantum systems of arbitrary finite dimension $d$. LAN means that the quantum statistical model consisting of $n$ identically prepared $d$-dimensional systems…
Given the failure of existing models for redshift-space distortions to provide a highly accurate measure of the beta-parameter, and the ability of forthcoming surveys to obtain data with very low random errors, it becomes necessary to…
We introduce DeepDFT, a deep learning model for predicting the electronic charge density around atoms, the fundamental variable in electronic structure simulations from which all ground state properties can be calculated. The model is…
Let $X(\cdot) $ be a random field $\mathbb{R}^D \to \mathbb{R}^d$, $D\geq d$. We first studied the level set $X^{-1}( u) $, $u \in \mathbb{R}^d$. In particular we gave a weak condition for this level set to be rectifiable. Then, we…
Kernel density estimation is a key component of a wide variety of algorithms in machine learning, Bayesian inference, stochastic dynamics and signal processing. However, the unsupervised density estimation technique requires tuning a…
We investigate the Hausdorff dimension of level sets defined by digit growth rates in $\theta$-expansions, a generalization of regular continued fractions. For any $\alpha \geq 0$, we prove that the set \[ E_\theta(\alpha) = \left\{ x \in…
Accurate forest canopy height estimation is essential for evaluating aboveground biomass and carbon stock dynamics, supporting ecosystem monitoring services like timber provisioning, climate change mitigation, and biodiversity conservation.…
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…
We consider the problem of estimating the density of observations taking values in classical or nonclassical spaces such as manifolds and more general metric spaces. Our setting is quite general but also sufficiently rich in allowing the…
It is common, in deconvolution problems, to assume that the measurement errors are identically distributed. In many real-life applications, however, this condition is not satisfied and the deconvolution estimators developed for…
We introduce a novel two-step approach for estimating a probability density function (pdf) given its samples, with the second and important step coming from a geometric formulation. The procedure involves obtaining an initial estimate of…
Many algorithms in machine learning and computational geometry require, as input, the intrinsic dimension of the manifold that supports the probability distribution of the data. This parameter is rarely known and therefore has to be…
High-dimensional data arises in numerous applications, and the rapidly developing field of geometric deep learning seeks to develop neural network architectures to analyze such data in non-Euclidean domains, such as graphs and manifolds.…