Related papers: Random Tessellations -- An Overview of Models
Structured latent attribute models (SLAMs) are a special family of discrete latent variable models widely used in social and biological sciences. This paper considers the problem of learning significant attribute patterns from a SLAM with…
This paper provides a tutorial discussion on analyzing structural equation modelling (SEM). SEM can be regarded as regression models with observed and unobserved indicators, have been extensively applied to practical and fundamental…
This paper introduces the Heteroscedastic AddiVortes model, a Bayesian non-parametric regression framework that simultaneously models the conditional mean and variance of a response variable using adaptive Voronoi tessellations. By…
Model stitching (Lenc & Vedaldi 2015) is a compelling methodology to compare different neural network representations, because it allows us to measure to what degree they may be interchanged. We expand on a previous work from Bansal,…
A system of nested dichotomies is a method of decomposing a multi-class problem into a collection of binary problems. Such a system recursively splits the set of classes into two subsets, and trains a binary classifier to distinguish…
Valuations, as additive functionals, allow various applications in Stochastic Geometry, yielding mean value formulas for specific random closed sets and processes of convex or polyconvex particles. In particular, valuations are especially…
Probabilistic graphical models combine the graph theory and probability theory to give a multivariate statistical modeling. They provide a unified description of uncertainty using probability and complexity using the graphical model.…
Stochastic dynamical systems arise naturally across nearly all areas of science and engineering. Typically, a dynamical system model is based on some prior knowledge about the underlying dynamics of interest in which probabilistic features…
We consider one-dimensional and two-dimensional models of the stochastic resin transfer molding process, which are formulated as random moving boundary problems. We study their properties, analytically in the one-dimensional case and…
In this paper, we construct a new family of random series defined on $\R^D$, indexed by one scaling parameter and two Hurst-like exponents. The model is close to Takagi-Knopp functions, save for the fact that the underlying partitions of…
A stochastic telegraph equation is defined by adding a random inhomogeneity to the classical (second order linear hyperbolic) telegraph differential equation. The inhomogeneities we consider are proportional to the two-dimensional white…
A projective rectangle is like a projective plane that has different lengths in two directions. We develop the basic theory of projective rectangles including incidence properties, projective subplanes, configuration counts, a partial…
Specify a randomized algorithm that, given a very large graph or network, extracts a random subgraph. What can we learn about the input graph from a single subsample? We derive laws of large numbers for the sampler output, by relating…
This article serves as an introduction to the study of networks of social systems. First, we introduce the reader to key mathematical tools to study social networks, including mathematical representations of networks and essential…
The past two decades have witnessed a surge of new research in the analysis of randomized experiments. The emergence of this literature may seem surprising given the widespread use and long history of experiments as the "gold standard" in…
Heterogeneity of many building materials complicates numerical modelling of structural behaviour. The material randomicity can be manifested by different values of material parameters of each material specimen. To capture inherent…
Random tensor networks are a powerful toy model for understanding the entanglement structure of holographic quantum gravity. However, unlike holographic quantum gravity, their entanglement spectra are flat. It has therefore been argued that…
We give a overview of stochastic models of evolution that have found applications in genetics, ecology and linguistics for an audience of nonspecialists, especially statistical physicists. In particular, we focus mostly on neutral models in…
For the analysis of systems consisting of small, regular objects, the methods of mathematical morphology applied to images of these systems are well-suited. One of these methods is the use of Voronoi polygons. It was found that the Voronoi…
A natural representation of random graphs is the random measure. The collection of product random measures, their transformations, and non-negative test functions forms a general representation of the collection of non-negative weighted…