Related papers: General hypergeometric distribution: A basic stati…
We study the mixing time of random graphs in the $d$-dimensional toric unit cube $[0,1]^d$ generated by the geographical threshold graph (GTG) model, a generalization of random geometric graphs (RGG). In a GTG, nodes are distributed in a…
Modelling of precipitation, including extremes, is important for hydrological and agricultural applications. Traditionally, because of large sample properties for data over a large threshold value, generalised Pareto (GP) distributions are…
A class of discrete probability distributions contains distributions with limited support. A typical example is some variant of a Likert scale, with response mapped to either the $\{1, 2, \ldots, 5\}$ or $\{-3, -2, \ldots, 2, 3\}$ set. An…
Integer sequences where each element is determined by a previous randomly chosen element are investigated analytically. In particular, the random geometric series x_n=2x_p with 0<=p<=n-1 is studied. At large n, the moments grow…
Interpreting graph neural networks (GNNs) is difficult because message passing mixes signals and internal channels rarely align with human concepts. We study superposition, the sharing of directions by multiple features, directly in the…
Modelling excesses over a high threshold using the Pareto or generalized Pareto distribution (PD/GPD) is the most popular approach in extreme value statistics. This method typically requires high thresholds in order for the (G)PD to fit…
Generalized linear models (GLM) are link function based statistical models. Many supervised learning algorithms are extensions of GLMs and have link functions built into the algorithm to model different outcome distributions. There are two…
In recent years, a number of methods have been developed to infer complex demographic histories, especially historical population size changes, from genomic sequence data. Coalescent Hidden Markov Models have proven to be particularly…
We introduce a broad class of random graph models: the generalised hypergeometric ensemble (GHypEG). This class enables to solve some long standing problems in random graph theory. First, GHypEG provides an elegant and compact formulation…
We propose an integral geometric approach for computing dual distributions for the parameter distributions of multilinear models. The dual distributions can be computed from, for example, the parameter distributions of conics, multiple view…
When assessing the impact of extreme events, it is often not just a single component, but the combined behaviour of several components which is important. Statistical modelling using multivariate generalized Pareto (GP) distributions…
Due to its heavy-tailed and fully parametric form, the multivariate generalized Gaussian distribution (MGGD) has been receiving much attention for modeling extreme events in signal and image processing applications. Considering the…
Random tensor networks provide useful models that incorporate various important features of holographic duality. A tensor network is usually defined for a fixed graph geometry specified by the connection of tensors. In this paper, we…
With generalizing the Brody distribution to include the Poisson, GOE and GUE limits and with employing the maximum likelihood estimation technique, the spectral statistics of different sequences were considered in the nearest neighbor…
The gravity model (GM) analogous to Newton's law of universal gravitation has successfully described the flow between different spatial regions, such as human migration, traffic flows, international economic trades, etc. This simple but…
Given two weighted k-uniform hypergraphs G, H of order n, how much (or little) can we make them overlap by placing them on the same vertex set? If we place them at random, how concentrated is the distribution of the intersection? The aim of…
Distributed averaging, or distributed average consensus, is a common method for computing the sample mean of the data dispersed among the nodes of a network in a decentralized manner. By iteratively exchanging messages with neighbors, the…
Multivariate generalized Pareto distributions arise as the limit distributions of exceedances over multivariate thresholds of random vectors in the domain of attraction of a max-stable distribution. These distributions can be parametrized…
We propose new generalized multivariate hypergeometric distributions, which extremely resemble the classical multivariate hypergeometric distributions. The proposed distributions are derived based on an urn model approach. In contrast to…
Data heterogeneity in federated learning, characterized by a significant misalignment between local and global distributions, leads to divergent local optimization directions and hinders global model training. Existing studies mainly focus…