Related papers: Geometric Representations of Random Hypergraphs

We present an algorithm to identify sparse dependence structure in continuous and non-Gaussian probability distributions, given a corresponding set of data. The conditional independence structure of an arbitrary distribution can be…

Understanding the data-generating process is essential for building machine learning models that generalise well while ensuring robustness and interpretability. This paper addresses the fundamental challenge of modelling the data generation…

Exchangeable random graphs serve as an important probabilistic framework for the statistical analysis of network data. In this work we develop an alternative parameterization for a large class of exchangeable random graphs, where the nodes…

Several types of graphs with different conditional independence interpretations --- also known as Markov properties --- have been proposed and used in graphical models. In this paper we unify these Markov properties by introducing a class…

Modeling and simulating movement of vehicles in established transportation infrastructures, especially in large urban road networks is an important task. It helps with understanding and handling traffic problems, optimizing traffic…

We improve the running time of the general algorithmic technique known as Baker's approach (1994) on H-minor-free graphs from O(n^{f(|H|)}) to O(f(|H|) n^{O(1)}). The numerous applications include e.g. a 2-approximation for coloring and…

Graphical Markov models combine conditional independence constraints with graphical representations of stepwise data generating processes.The models started to be formulated about 40 years ago and vigorous development is ongoing.…

We develop a new Markov chain on graph partitions that makes relatively global moves yet is computationally feasible to be used as the proposal in the Metropolis-Hastings method. Our resulting algorithm can be made reversible and able to…

We show that contiguity relations of hypergeometric functions of several variables give a direct sampling algorithm from the conditional distribution of toric models in statistics. The algorithm is based on a Markov chain on a lattice…

In the recent years we have witnessed a rapid development of new algorithmic techniques for parameterized algorithms for graph separation problems. We present experimental evaluation of two cornerstone theoretical results in this area:…

We propose prior distributions for all parts of the specification of a Markov mesh model. In the formulation we define priors for the sequential neighborhood, for the parametric form of the conditional distributions and for the parameter…

Representing the conditional independences present in a multivariate random vector via graphs has found widespread use in applications, and such representations are popularly known as graphical models or Markov random fields. These models…

Dense disparities among multiple views is essential for estimating the 3D architecture of a scene based on the geometrical relationship among the scene and the views or cameras. Scenes with larger extents of heterogeneous textures,…

High-dimensional data analysis typically focuses on low-dimensional structure, often to aid interpretation and computational efficiency. Graphical models provide a powerful methodology for learning the conditional independence structure in…

Consider a collection of random variables attached to the vertices of a graph. The reconstruction problem requires to estimate one of them given `far away' observations. Several theoretical results (and simple algorithms) are available when…

Statistical models for multivariate data often include a semi-orthogonal matrix parameter. In many applications, there is reason to expect that the semi-orthogonal matrix parameter satisfies a structural assumption such as sparsity or…

Hypergraphs capture multi-way relationships in data, and they have consequently seen a number of applications in higher-order network analysis, computer vision, geometry processing, and machine learning. In this paper, we develop…

Prior specifications for hyperparameters of random fields in Bayesian spatial point process modelling can have a major impact on the statistical inference and the conclusions made. We consider fitting of log-Gaussian Cox processes to…

Pairwise Markov Random Fields (MRFs) or undirected graphical models are parsimonious representations of joint probability distributions. Variables correspond to nodes of a graph, with edges between nodes corresponding to conditional…

We study the Induced $H$ Partition problem from the parameterized complexity point of view. In the Induced $H$ Partition problem the task is to partition vertices of a graph $G$ into sets $V_1,V_2,\dots,V_n$ such that the graph $H$ is…