Related papers: Density estimation via mixture discrepancy and mom…
Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…
Gaussian mixture filters for nonlinear systems usually rely on severe approximations when calculating mixtures in the prediction and filtering step. Thus, offline approximations of noise densities by Gaussian mixture densities to reduce the…
We study the problem of optimal estimation of the density cluster tree under various assumptions on the underlying density. Building up from the seminal work of Chaudhuri et al. [2014], we formulate a new notion of clustering consistency…
How to create planetesimals from tiny dust particles in a proto-planetary disk before the dust particles spiral to the central star is one of the most challenging problems in the theory of planetary system formation. In our previous paper…
Some aspects of the systematic and statistical errors affecting grid-based estimation of stellar masses and radii have still not been investigated well. We study the impact on mass and radius determination of the uncertainty in the input…
Diffusion models have emerged as powerful generative priors for solving inverse imaging problems. However, their practical deployment is hindered by the substantial computational cost of slow, multi-step sampling. Although Consistency…
Here we introduce the Delaunay Density Estimator Method. Its purpose is rendering a fully volume-covering reconstruction of a density field from a set of discrete data points sampling this field. Reconstructing density or intensity fields…
We introduce the so called DeepParticle method to learn and generate invariant measures of stochastic dynamical systems with physical parameters based on data computed from an interacting particle method (IPM). We utilize the expressiveness…
The distribution of dark matter (DM) inside galaxies is not uniform. Near the central regions, its density is the highest. Then, it is logical to suppose that, inside galaxies, DM affects the physics of stars in central regions more than…
Depth completion involves estimating a dense depth image from sparse depth measurements, often guided by a color image. While linear upsampling is straight forward, it results in artifacts including depth pixels being interpolated in empty…
Mixture distributions are a workhorse model for multimodal data in information theory, signal processing, and machine learning. Yet even when each component density is simple, the differential entropy of the mixture is notoriously hard to…
Identifying spatially contiguous clusters and repeated spatial patterns (RSP) characterized by similar underlying distributions that are spatially apart is a key challenge in modern spatial statistics. Existing constrained clustering…
In model-based clustering using finite mixture models, it is a significant challenge to determine the number of clusters (cluster size). It used to be equal to the number of mixture components (mixture size); however, this may not be valid…
We establish a novel criterion for comparing the performance of two densities, $g_1$ and $g_2$, within the context of corrupted data. Utilizing this criterion, we propose an algorithm to construct a density estimator within a star-shaped…
Validation of image segmentation methods is of critical importance. Probabilistic image segmentation is increasingly popular as it captures uncertainty in the results. Image segmentation methods that support multi-region (as opposed to…
We introduce a method for generating a continuous, mass-conserving and high-order differentiable density field from a discrete point distribution such as particles or halos from an N-body simulation or galaxies from a spectroscopic survey.…
Scale invariance (fractality) is a prominent feature of the large-scale behavior of many stochastic systems. In this work, we construct an algorithm for the statistical identification of the Hurst distribution (in particular, the scaling…
We propose a goodness-of-fit measure for probability densities modeling observations with varying dimensionality, such as text documents of differing lengths or variable-length sequences. The proposed measure is an instance of the kernel…
High-dimensional clustering analysis is a challenging problem in statistics and machine learning, with broad applications such as the analysis of microarray data and RNA-seq data. In this paper, we propose a new clustering procedure called…
Grouped data are commonly encountered in applications. The Bernstein polynomial model is proposed as an approximate model in this paper for estimating a univariate density function based on grouped data. The coefficients of the Bernstein…