Related papers: Groups acting on Gaussian graphical models
We define a new diffusive matrix model converging towards the $\beta$ -Dyson Brownian motion for all $\beta\in [0,2]$ that provides an explicit construction of $\beta$-ensembles of random matrices that is invariant under the…
A finite graph $\Gamma$ is called $G$-symmetric if $G$ is a group of automorphisms of $\Gamma$ which is transitive on the set of ordered pairs of adjacent vertices of $\Gamma$. We study a family of symmetric graphs, called the unitary…
Gaussian Boson Samplers aim to demonstrate quantum advantage by performing a sampling task believed to be classically hard. The probabilities of individual outcomes in the sampling experiment are determined by the Hafnian of an…
For plane frameworks with reflection or rotational symmetries, where the group action is not necessarily free on the vertex set, we introduce a phase-symmetric orbit rigidity matrix for each irreducible representation of the group. We then…
Gaussian graphical models (GGMs) are widely used to recover the conditional independence structure among random variables. Recent work has sought to incorporate auxiliary covariates to improve estimation, particularly in applications such…
Gaussian Graphical Model selection problem is considered. Concentration graph is identified by multiple decision procedure based on individual tests. Optimal unbiased individual tests are constructed. It is shown that optimal tests are…
We have generalised the concept of graph states to what we have called mixed graph states, which we define in terms of mixed graphs, that is graphs with both directed and undirected edges, as the density matrix stabilized by the associated…
We study properties of the realizations of groups as the combinatorial automorphism group of a convex polytope. We show that for any non-abelian group $G$ with a central involution there is a centrally symmetric polytope with $G$ as its…
We consider the problem of learning a conditional Gaussian graphical model in the presence of latent variables. Building on recent advances in this field, we suggest a method that decomposes the parameters of a conditional Markov random…
An important task in data analysis is the discovery of causal relationships between observed variables. For continuous-valued data, linear acyclic causal models are commonly used to model the data-generating process, and the inference of…
We study gauge theory with finite group $G$ on a graph $X$ using noncommutative differential geometry and Hopf algebra methods with $G$-valued holonomies replaced by gauge fields valued in a `finite group Lie algebra' subset of the group…
We study discrete, cocompact, isometric actions of groups on Hadamard spaces, and the induced actions on ideal boundaries. For a class of groups generalizing fundamental groups of three-dimensional graph manifolds, we find a set of…
The success of machine learning methods heavily relies on having an appropriate representation for data at hand. Traditionally, machine learning approaches relied on user-defined heuristics to extract features encoding structural…
Graphs are one of the most important data structures for representing pairwise relations between objects. Specifically, a graph embedded in a Euclidean space is essential to solving real problems, such as physical simulations. A crucial…
A famously hard graph problem with a broad range of applications is computing the number of perfect matchings, that is the number of unique and complete pairings of the vertices of a graph. We propose a method to estimate the number of…
Graphical models are ubiquitous tools to describe the interdependence between variables measured simultaneously such as large-scale gene or protein expression data. Gaussian graphical models (GGMs) are well-established tools for…
We consider the scaling limit of linear statistics for eigenphases of a matrix taken from one of the classical compact groups. We compute their moments and find that the first few moments are Gaussian, whereas the limiting distribution is…
Gaussian processes (GPs) are pervasive in functional data analysis, machine learning, and spatial statistics for modeling complex dependencies. Modern scientific data sets are typically heterogeneous and often contain multiple known…
In Gaussian graphical models, the likelihood equations must typically be solved iteratively. We investigate two algorithms: A version of iterative proportional scaling which avoids inversion of large matrices, and an algorithm based on…
We investigate the nodal count of eigenvectors of random matrices interpreted as operators on signed complete graphs. Our focus is on orthogonally invariant ensembles, with particular attention to the Gaussian Orthogonal Ensemble (GOE). We…