Related papers: GET: Global envelopes in R
We present a program package which generates homogeneous random graphs with probabilities prescribed by the user. The statistical weight of a labeled graph $\alpha$ is given in the form $W(\alpha)=\prod_{i=1}^N p(q_i)$, where $p(q)$ is an…
The g-and-k and (generalised) g-and-h distributions are flexible univariate distributions which can model highly skewed or heavy tailed data through only four parameters: location and scale, and two shape parameters influencing the skewness…
Spectral embedding is a procedure which can be used to obtain vector representations of the nodes of a graph. This paper proposes a generalisation of the latent position network model known as the random dot product graph, to allow…
A major effort in modern high-dimensional statistics has been devoted to the analysis of linear predictors trained on nonlinear feature embeddings via empirical risk minimization (ERM). Gaussian equivalence theory (GET) has emerged as a…
Entropy integrals are widely used as a powerful empirical process tool to obtain upper bounds for the rates of convergence of global empirical risk minimizers (ERMs), in standard settings such as density estimation and regression. The upper…
A framework (a straight-line embedding of a graph into a normed space allowing edges to cross) is globally rigid if any other framework with the same edge lengths with respect to the chosen norm is an isometric copy. We investigate global…
Envelopes were recently proposed as methods for reducing estimative variation in multivariate linear regression. Estimation of an envelope usually involves optimization over Grassmann manifolds. We propose a fast and widely applicable…
Global constraints proved themselves to be an efficient tool for modelling and solving large-scale real-life combinatorial problems. They encapsulate a set of binary constraints and using global reasoning about this set they filter the…
We introduce a model for a growing random graph based on simultaneous reproduction of the vertices. The model can be thought of as a generalisation of the reproducing graphs of Southwell and Cannings and Bonato et al to allow for a random…
A generalization of the random geometric graph (RGG) model is proposed by considering a set of points uniformly and independently distributed on a rectangle of unit area instead of on a unit square [0,1]^2. The topological properties of the…
We describe the open-source global fitting package GAMBIT: the Global And Modular Beyond-the-Standard-Model Inference Tool. GAMBIT combines extensive calculations of observables and likelihoods in particle and astroparticle physics with a…
Probabilistic graphical models with frustration exhibit rugged energy landscapes that trap iterative optimization dynamics. These landscapes are shaped not only by local interactions, but crucially also by the global loop structure of the…
R2BEAT (R "to" Bethel Extended Allocation for Two-stage sampling) is an R package for the allocation of a sample. Besides other software and packages dealing with the allocation problems, its peculiarity lies in facing properly allocation…
Geometry constitutes a core set of intuitions present in all humans, regardless of their language or schooling [1]. Could brain's built in machinery for processing geometric information take part in uncertainty representation? For decades…
Networks constitute efficient tools for assessing universal features of complex systems. In physical contexts, classical as well as quantum, networks are used to describe a wide range of phenomena, such as phase transitions, intricate…
In this paper we use Gaussian Process (GP) regression to propose a novel approach for predicting volatility of financial returns by forecasting the envelopes of the time series. We provide a direct comparison of their performance to…
Generalised degrees provide a natural bridge between local and global topological properties of networks. We define the generalised degree to be the number of neighbours of a node within one and two steps respectively. Tailored random graph…
Recent work on graph generative models has made remarkable progress towards generating increasingly realistic graphs, as measured by global graph features such as degree distribution, density, and clustering coefficients. Deep generative…
iGraphMatch is an R package for finding corresponding vertices between two graphs, also known as graph matching. The package implements three categories of prevalent graph matching algorithms including relaxation-based, percolation-based,…
We show that any graph that is generically globally rigid in $\mathbb{R}^d$ has a realization in $\mathbb{R}^d$ that is both generic and universally rigid. This also implies that the graph also must have a realization in $\mathbb{R}^d$ that…