Related papers: Gibbs cluster measures on configuration spaces

Mixture model-based frameworks are very popular for statistical inference in clustering. While convenient for producing probabilistic estimates of cluster assignments and uncertainty, they are prone to misspecification, which can lead to…

We develop methods for efficient amortized approximate Bayesian inference over posterior distributions of probabilistic clustering models, such as Dirichlet process mixture models. The approach is based on mapping distributed,…

We discuss the $(1+1)$-dimensional wave maps equation with values in a compact Lie group. The corresponding Gibbs measure is given by a Brownian motion on the Lie group, which plays a central role in stochastic geometry. Our main theorem is…

We carry out analysis and geometry on a marked configuration space $\Omega_X^{R_+}$ over a Riemannian manifold $X$ with marks from the space $R_+$ as a natural generalization of the work {\bf [}{\it J. Func. Anal}. {\bf 154} (1998),…

To identify novel dynamic patterns of gene expression, we develop a statistical method to cluster noisy measurements of gene expression collected from multiple replicates at multiple time points, with an unknown number of clusters. We…

The parsimonious Gaussian mixture models, which exploit an eigenvalue decomposition of the group covariance matrices of the Gaussian mixture, have shown their success in particular in cluster analysis. Their estimation is in general…

We study the problem of posterior sampling in discrete-state spaces using discrete diffusion models. While posterior sampling methods for continuous diffusion models have achieved remarkable progress, analogous methods for discrete…

We consider the problem of analyzing the heterogeneity of clustering distributions for multiple groups of observed data, each of which is indexed by a covariate value, and inferring global clusters arising from observations aggregated over…

Motivated by the need to model the dependence between regions of interest in functional neuroconnectivity for efficient inference, we propose a new sampling-based Bayesian clustering approach for covariance structures of high-dimensional…

The abundance and mass distribution of galaxy clusters is a sensitive probe of cosmological parameters, through the sensitivity of the high-mass end of the halo mass function to $\Omega_m$ and $\sigma_8$. While galaxy cluster surveys have…

Clustering multivariate data is a pervasive task in many applied problems, particularly in social studies and life science. Model-based approaches to clustering rely on mixture models, where each mixture component corresponds to the kernel…

The concept of metastate measures on the states of a random spin system was introduced to be able to treat the large-volume asymptotics for complex quenched random systems, like spin glasses, which may exhibit chaotic volume dependence in…

Model sets play a fundamental role in structure analysis of quasicrystals. The diffraction diagram of a quasicrystal admits as symmetry group a finite group G, and there is a G-cluster C (union of orbits of G) such that the quasicrystal can…

Gravitational lensing by clusters of galaxies has been detected on scales ranging from $\sim10^{-1}$ Mpc to $\sim10$ Mpc, namely, arcs/arclets, weak lensing and quasar-cluster associations. This allows us to derive an overall radius matter…

In order to quantify higher-order correlations of the galaxy cluster distribution we use a complete family of additive measures which give scale-dependent morphological information. Minkowski functionals can be expressed analytically in…

We derive the 1-point probability density function of the smoothed 3-D Abell-ACO cluster density field and we compare it with that of artificial cluster samples, generated as high peaks of a Gaussian field in such a way that they reproduce…

Approximate Bayesian computation methods are useful for generative models with intractable likelihoods. These methods are however sensitive to the dimension of the parameter space, requiring exponentially increasing resources as this…

For a locally compact group $G$ and a strongly self-absorbing $G$-algebra $(\mathcal{D},\delta)$, we obtain a new characterization of absorption of a strongly self-absorbing action using almost equivariant completely positive maps into the…

We study Gibbs measures with log-correlated base Gaussian fields on the $d$-dimensional torus. In the defocusing case, the construction of such Gibbs measures follows from Nelson's argument. In this paper, we consider the focusing case with…

We give an efficient algorithm for robustly clustering of a mixture of two arbitrary Gaussians, a central open problem in the theory of computationally efficient robust estimation, assuming only that the the means of the component Gaussians…